Wstęp
Opis problemu
Problemem, który analizujemy w niniejszym projekcie jest wpływ poszczególnych czynników na wynik końcowy ucznia (?)
Baza danych
Baza danych którą analizujemy nazywa się „Wyniki uczniów”. Znajduje się w niej 20 kolumn z danymi oraz 6.608 wierszy danych. W bazie danych znajdują się zarówno zmienne liczbowe jak i jakościowe.
czynniki <- read.csv("czynniki.csv")
glimpse(czynniki)## Rows: 6,607
## Columns: 20
## $ Hours_Studied <int> 23, 19, 24, 29, 19, 19, 29, 25, 17, 23, 17,…
## $ Attendance <int> 84, 64, 98, 89, 92, 88, 84, 78, 94, 98, 80,…
## $ Parental_Involvement <chr> "Low", "Low", "Medium", "Low", "Medium", "M…
## $ Access_to_Resources <chr> "High", "Medium", "Medium", "Medium", "Medi…
## $ Extracurricular_Activities <chr> "No", "No", "Yes", "Yes", "Yes", "Yes", "Ye…
## $ Sleep_Hours <int> 7, 8, 7, 8, 6, 8, NA, 6, 6, 8, 8, 6, 8, 8, …
## $ Previous_Scores <int> 73, 59, 91, 98, 65, 89, 68, 50, 80, 71, 88,…
## $ Motivation_Level <chr> "Low", "Low", "Medium", "Medium", "Medium",…
## $ Internet_Access <chr> "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "…
## $ Tutoring_Sessions <int> 0, 2, 2, 1, 3, 3, 1, 1, 0, 0, 4, 2, 2, 2, 1…
## $ Family_Income <chr> "Low", "Medium", "Medium", "Medium", "Mediu…
## $ Teacher_Quality <chr> "Medium", "Medium", "Medium", "Medium", "Hi…
## $ School_Type <chr> "Public", "Public", "Public", "Public", "Pu…
## $ Peer_Influence <chr> "Positive", "Negative", "Neutral", "Negativ…
## $ Physical_Activity <int> 3, 4, 4, 4, 4, 3, 2, 2, 1, 5, 4, 2, 4, 3, 4…
## $ Learning_Disabilities <chr> "No", "No", "No", "No", "No", "No", "No", "…
## $ Parental_Education_Level <chr> "High School", "College", "Postgraduate", "…
## $ Distance_from_Home <chr> "Near", "Moderate", "Near", "Moderate", "Ne…
## $ Gender <chr> "Male", "Female", "Male", "Male", "Female",…
## $ Exam_Score <int> 67, 61, 74, 71, NA, 71, 67, 66, 69, 72, 68,…Czyszczenie danych
W niniejszym rozdziale sprawdzimy jakość danych, zbadamy występowanie braków danych oraz dobierzemy odpowiednią metodę imputacji brakujących danych (jeżeli zajdzie taka potrzeba).
Walidacja danych
Zostało wykonane badanie danych za pomocą funkcji aggr. Wykres po lewej stronie prezentuje proporcje braków danych. W naszym przypadku największe braki występują w trzech zmiennych:
- Sleep Hours - 5,22%
- Exam Score - 4,37%
- Distance from Home - 1,01%
Tabela po prawej stronie ilistruje współwystępowanie braków w zestawie danych. Czerwone pola oznaczają brakujące wartości. Można zauważyć, że brakujące dane są dość rozporoszone i nie występują jednocześnie w wielu zmiennych. Oznacza to, że nie instnieje współzależność pomiędzy występowaniem braków więc dane brakujące będziemy uzupełniać za pomocą podobieństwa.
aggr(czynniki, numbers = TRUE, sortVars = TRUE)
##
## Variables sorted by number of missings:
## Variable Count
## Sleep_Hours 0.05297412
## Family_Income 0.05297412
## Exam_Score 0.04540639
## Parental_Education_Level 0.01362192
## Teacher_Quality 0.01180566
## Distance_from_Home 0.01014076
## Hours_Studied 0.00000000
## Attendance 0.00000000
## Parental_Involvement 0.00000000
## Access_to_Resources 0.00000000
## Extracurricular_Activities 0.00000000
## Previous_Scores 0.00000000
## Motivation_Level 0.00000000
## Internet_Access 0.00000000
## Tutoring_Sessions 0.00000000
## School_Type 0.00000000
## Peer_Influence 0.00000000
## Physical_Activity 0.00000000
## Learning_Disabilities 0.00000000
## Gender 0.00000000gg_miss_upset(czynniki)
Wykres poniżej został stworzony za pomocą funkcji gg_miss_upset. Prezentuje on wartości liczbowe brakujących danych
- Family income – 309
- Sleep Hours – 300
Z uwagi na stosunkowo wysoką ilość braków dokonamy imputacji danych.
czynniki1<- czynniki[!is.na(czynniki$Family_Income), ]
czynniki2<- czynniki1[!is.na(czynniki1$Parental_Education_Level), ]
czynniki3<- czynniki2[!is.na(czynniki2$Teacher_Quality), ]
czynniki4<- czynniki3[!is.na(czynniki3$Distance_from_Home), ]
unique(czynniki4$Family_Income)## [1] "Low" "Medium" "High"unique(czynniki4$Parental_Education_Level)## [1] "High School" "College" "Postgraduate"unique(czynniki4$Teacher_Quality)## [1] "Medium" "High" "Low"unique(czynniki4$Distance_from_Home)## [1] "Near" "Moderate" "Far"glimpse(czynniki4)## Rows: 6,038
## Columns: 20
## $ Hours_Studied <int> 23, 19, 24, 29, 19, 19, 29, 25, 17, 17, 17,…
## $ Attendance <int> 84, 64, 98, 89, 92, 88, 84, 78, 94, 80, 97,…
## $ Parental_Involvement <chr> "Low", "Low", "Medium", "Low", "Medium", "M…
## $ Access_to_Resources <chr> "High", "Medium", "Medium", "Medium", "Medi…
## $ Extracurricular_Activities <chr> "No", "No", "Yes", "Yes", "Yes", "Yes", "Ye…
## $ Sleep_Hours <int> 7, 8, 7, 8, 6, 8, NA, 6, 6, 8, 6, 8, 8, NA,…
## $ Previous_Scores <int> 73, 59, 91, 98, 65, 89, 68, 50, 80, 88, 87,…
## $ Motivation_Level <chr> "Low", "Low", "Medium", "Medium", "Medium",…
## $ Internet_Access <chr> "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "…
## $ Tutoring_Sessions <int> 0, 2, 2, 1, 3, 3, 1, 1, 0, 4, 2, 2, 2, 1, 2…
## $ Family_Income <chr> "Low", "Medium", "Medium", "Medium", "Mediu…
## $ Teacher_Quality <chr> "Medium", "Medium", "Medium", "Medium", "Hi…
## $ School_Type <chr> "Public", "Public", "Public", "Public", "Pu…
## $ Peer_Influence <chr> "Positive", "Negative", "Neutral", "Negativ…
## $ Physical_Activity <int> 3, 4, 4, 4, 4, 3, 2, 2, 1, 4, 2, 4, 3, 4, 4…
## $ Learning_Disabilities <chr> "No", "No", "No", "No", "No", "No", "No", "…
## $ Parental_Education_Level <chr> "High School", "College", "Postgraduate", "…
## $ Distance_from_Home <chr> "Near", "Moderate", "Near", "Moderate", "Ne…
## $ Gender <chr> "Male", "Female", "Male", "Male", "Female",…
## $ Exam_Score <int> 67, 61, 74, 71, NA, 71, 67, 66, 69, 68, 71,…gg_miss_upset(czynniki4)
aggr(czynniki4, numbers = TRUE, sortVars = TRUE)
##
## Variables sorted by number of missings:
## Variable Count
## Sleep_Hours 0.05266645
## Exam_Score 0.04372309
## Hours_Studied 0.00000000
## Attendance 0.00000000
## Parental_Involvement 0.00000000
## Access_to_Resources 0.00000000
## Extracurricular_Activities 0.00000000
## Previous_Scores 0.00000000
## Motivation_Level 0.00000000
## Internet_Access 0.00000000
## Tutoring_Sessions 0.00000000
## Family_Income 0.00000000
## Teacher_Quality 0.00000000
## School_Type 0.00000000
## Peer_Influence 0.00000000
## Physical_Activity 0.00000000
## Learning_Disabilities 0.00000000
## Parental_Education_Level 0.00000000
## Distance_from_Home 0.00000000
## Gender 0.00000000Imputacja danych
as.numeric(czynniki4$Exam_Score)## [1] 67 61 74 71 NA 71 67 66 69 68 71 70 66 65 64 60 65 67
## [19] 66 69 72 66 66 63 65 71 66 64 69 67 68 61 64 67 63 NA
## [37] 67 65 64 70 68 65 68 64 68 63 64 67 67 66 72 65 71 66
## [55] 68 70 62 68 71 68 69 NA 69 65 70 71 65 72 69 66 68 65
## [73] 60 65 66 74 62 70 69 67 64 71 68 64 63 71 69 100 68 62
## [91] 68 66 64 67 65 65 69 63 72 76 69 67 69 63 67 66 79 64
## [109] 73 63 65 73 70 68 71 64 68 69 NA 67 68 64 66 63 66 66
## [127] 67 65 68 68 65 71 65 64 72 65 66 61 68 69 71 70 68 67
## [145] 68 68 72 65 66 65 67 NA 69 66 69 67 66 71 70 71 66 67
## [163] 66 72 68 69 71 70 67 69 65 65 64 63 69 64 72 63 64 64
## [181] 67 71 70 61 67 72 66 70 67 67 71 66 68 74 64 65 66 66
## [199] 68 78 67 74 74 62 66 69 68 89 66 68 67 75 60 66 73 68
## [217] 62 62 65 69 64 67 70 70 69 61 69 63 67 66 63 68 65 67
## [235] 68 64 71 69 67 65 68 67 67 66 70 65 69 65 63 67 61 65
## [253] 66 66 69 63 65 67 69 65 65 65 67 72 NA 65 69 68 64 59
## [271] 68 60 62 67 68 64 65 65 63 70 66 66 63 66 65 NA 67 66
## [289] 63 NA 67 71 67 69 67 72 70 67 64 67 69 63 68 70 66 68
## [307] 67 69 66 68 69 70 74 70 66 69 64 62 70 68 65 NA 71 66
## [325] 61 67 65 65 NA 62 60 61 67 70 69 66 64 68 67 64 65 66
## [343] 68 66 63 63 74 70 66 63 67 71 NA 72 68 66 70 66 72 61
## [361] 62 68 68 63 70 68 72 67 61 69 75 NA 65 75 64 70 67 63
## [379] 67 86 67 63 66 67 NA 66 64 73 68 70 67 62 68 72 69 66
## [397] 70 71 65 70 65 62 62 70 66 67 72 66 68 62 64 65 66 67
## [415] 69 68 64 68 64 71 61 68 64 72 NA 68 NA 66 63 74 63 72
## [433] 69 67 66 64 67 69 64 65 72 66 66 67 69 73 69 68 61 63
## [451] 68 63 65 68 66 66 70 61 71 70 69 61 68 74 67 70 64 66
## [469] 63 61 68 65 69 68 69 70 68 67 67 75 70 70 64 59 63 67
## [487] 68 68 97 66 61 70 65 64 69 64 61 64 68 67 62 66 72 71
## [505] 65 68 65 64 65 65 73 72 64 69 69 70 83 68 84 75 67 69
## [523] 66 65 70 66 74 68 68 62 71 63 69 71 66 64 65 69 66 67
## [541] 65 65 67 66 69 70 68 70 67 72 69 69 64 63 70 70 66 70
## [559] 66 68 61 NA 69 72 65 74 62 65 68 71 NA 65 68 70 63 63
## [577] 69 66 70 63 72 63 65 NA 80 68 64 73 66 66 66 59 68 67
## [595] 64 65 68 70 NA 72 62 68 73 69 67 65 63 66 66 70 69 70
## [613] 58 67 66 70 67 60 65 63 72 NA 70 70 64 64 72 66 66 71
## [631] 66 64 66 62 70 69 65 70 70 67 69 62 67 65 65 69 63 66
## [649] 67 69 67 70 67 70 65 63 NA 69 60 69 72 63 63 70 NA 69
## [667] 72 67 68 70 68 69 68 66 72 67 70 73 73 60 67 69 65 65
## [685] 64 67 65 64 67 70 63 71 68 67 67 68 66 68 70 67 67 62
## [703] 67 70 72 70 94 66 69 68 71 69 67 64 63 66 69 64 62 70
## [721] 67 68 62 68 64 64 66 72 72 66 NA 69 72 69 69 62 70 68
## [739] 68 70 65 73 66 71 62 68 70 68 70 72 69 63 62 68 69 68
## [757] 65 59 66 63 72 NA 94 70 66 69 64 63 71 65 68 64 64 67
## [775] 66 NA 66 71 71 68 64 67 64 68 62 64 68 69 65 67 71 65
## [793] 65 65 68 68 67 65 66 63 72 67 67 66 66 69 62 66 64 67
## [811] 71 68 66 75 72 68 68 69 63 70 66 66 71 72 69 71 69 68
## [829] NA 68 72 70 73 67 65 68 65 NA 66 67 70 NA 69 62 68 67
## [847] 68 69 62 75 65 63 66 71 66 NA 66 68 71 68 68 62 65 71
## [865] 63 68 69 69 71 71 62 NA 70 71 69 65 71 68 64 67 NA 71
## [883] 62 67 66 NA 65 64 65 68 72 64 62 69 64 61 72 66 69 65
## [901] 64 66 62 66 70 75 67 66 NA NA 72 65 67 63 62 69 70 63
## [919] 71 63 71 63 65 66 66 66 66 67 68 68 69 64 67 63 64 66
## [937] 65 68 66 71 74 65 68 68 72 NA 61 65 63 66 66 73 63 73
## [955] 63 65 65 66 65 70 68 64 68 62 61 69 65 65 NA 70 65 69
## [973] 65 69 65 72 70 64 67 69 70 65 69 74 66 72 75 70 63 65
## [991] 64 NA NA 67 67 68 65 61 63 80 69 NA 70 65 68 64 69 89
## [1009] 67 92 67 70 68 70 67 69 67 69 63 66 68 69 66 72 62 67
## [1027] 67 67 65 67 66 70 71 64 72 60 71 71 NA 74 64 68 66 64
## [1045] 65 69 63 65 62 67 64 61 65 70 59 75 67 64 72 76 69 65
## [1063] 72 69 71 64 74 68 66 65 67 69 66 67 64 67 NA 68 66 66
## [1081] 63 66 66 65 69 71 66 66 65 71 69 61 70 70 65 64 68 63
## [1099] 71 58 68 65 65 68 69 71 65 64 75 67 68 NA 67 72 69 68
## [1117] 70 69 63 61 66 73 67 72 69 69 63 67 63 66 62 68 65 59
## [1135] 72 63 68 61 65 68 61 67 66 75 68 65 NA 64 67 63 67 65
## [1153] 62 69 70 68 68 64 63 68 67 68 66 67 69 70 68 66 67 65
## [1171] 67 63 64 64 66 68 67 72 67 66 66 67 65 70 69 69 66 66
## [1189] 67 67 67 72 68 70 69 65 72 69 68 62 60 67 67 67 63 71
## [1207] 66 65 69 63 64 67 62 68 66 69 71 66 70 65 64 63 63 66
## [1225] 68 74 71 67 66 67 62 68 62 82 70 NA 64 66 68 64 61 69
## [1243] 64 67 67 65 68 67 64 70 69 66 69 66 73 66 69 70 71 70
## [1261] 69 63 NA 73 68 69 76 68 65 65 69 66 69 59 65 NA 64 69
## [1279] 70 67 67 NA 68 72 65 NA 75 65 63 71 66 69 68 71 77 70
## [1297] 66 NA NA NA 66 72 NA 63 72 71 72 65 67 68 66 71 70 68
## [1315] 72 66 65 62 69 65 69 69 75 70 74 65 63 74 67 71 68 69
## [1333] 71 66 65 66 65 67 70 63 64 71 68 72 71 64 64 66 68 65
## [1351] 67 64 70 65 65 68 61 69 64 69 67 NA 66 72 73 73 63 69
## [1369] 71 63 69 72 68 62 68 71 67 65 68 59 71 70 62 62 68 68
## [1387] 61 67 65 101 65 67 NA NA 64 67 69 67 62 66 72 67 66 67
## [1405] 67 68 63 NA 65 65 70 73 73 68 63 62 69 66 68 67 65 70
## [1423] 64 65 67 62 66 68 64 69 67 61 70 65 66 66 69 67 71 68
## [1441] 67 63 64 73 69 65 70 67 67 NA 69 68 NA 67 71 68 66 64
## [1459] 71 61 67 65 66 68 66 63 66 73 88 67 69 67 64 64 65 68
## [1477] 77 63 69 70 73 NA 71 66 71 66 63 70 66 66 66 62 69 63
## [1495] 68 NA 69 71 71 66 72 70 71 65 65 68 70 70 72 65 65 71
## [1513] 64 65 73 72 65 66 66 68 67 65 64 70 63 65 67 71 73 67
## [1531] 72 71 72 68 65 68 67 66 64 65 69 68 69 70 65 71 68 70
## [1549] 72 NA 64 NA NA 71 69 67 66 71 63 62 NA 66 72 67 65 66
## [1567] 68 69 68 61 68 64 67 68 61 66 64 67 64 72 62 63 70 69
## [1585] 64 66 67 71 70 69 64 70 69 60 65 67 66 68 58 67 62 69
## [1603] 73 66 67 71 NA 74 67 68 61 65 71 61 70 70 69 70 67 63
## [1621] 70 61 64 65 65 66 66 63 66 64 65 62 71 63 70 70 65 68
## [1639] 68 NA 71 68 67 72 68 60 68 NA 67 70 70 68 67 62 66 69
## [1657] 66 64 66 63 62 65 68 65 63 68 72 69 66 68 64 61 67 68
## [1675] 74 67 64 69 63 67 65 67 62 70 67 NA 65 69 64 74 64 64
## [1693] 67 63 68 66 68 68 69 71 65 67 65 65 80 74 59 69 66 66
## [1711] 65 67 69 68 73 71 67 67 66 63 65 NA 69 67 66 66 69 63
## [1729] 64 64 69 73 62 62 66 68 66 NA 62 NA 67 65 69 67 64 62
## [1747] 71 72 74 66 72 65 70 62 65 70 69 70 66 73 69 66 65 70
## [1765] 70 67 68 68 61 70 65 66 67 69 69 67 66 63 67 64 68 65
## [1783] 65 70 62 68 62 68 70 NA 73 68 68 69 63 74 61 69 64 63
## [1801] 68 72 69 70 63 62 72 69 66 71 62 68 63 66 NA 69 68 69
## [1819] 67 73 71 71 68 70 71 NA 63 71 69 71 68 68 66 67 59 66
## [1837] 64 NA 69 69 61 62 61 63 71 NA 68 67 70 64 71 71 67 63
## [1855] 66 70 70 67 69 66 67 65 72 68 72 76 65 68 65 66 63 63
## [1873] 66 72 64 67 66 68 65 71 62 69 65 70 70 70 69 NA 69 73
## [1891] 65 62 67 65 65 70 70 71 71 NA 65 84 68 70 68 67 69 68
## [1909] 59 67 NA 63 64 NA 66 67 66 66 68 66 68 65 67 64 59 60
## [1927] 65 66 65 69 62 60 68 64 73 64 63 65 65 67 66 65 66 66
## [1945] 70 71 70 68 NA 68 66 67 66 69 67 61 70 70 70 64 65 70
## [1963] 62 64 67 62 72 69 72 68 64 72 73 67 64 NA 67 68 71 NA
## [1981] 59 68 64 70 65 72 66 68 62 70 70 64 76 67 68 67 69 67
## [1999] 73 71 70 73 65 70 66 64 68 70 72 66 74 67 NA 60 69 71
## [2017] 66 65 60 69 69 67 65 70 71 73 70 67 67 65 68 74 68 61
## [2035] 67 66 69 62 71 71 72 69 67 NA 68 69 65 70 65 67 72 69
## [2053] 69 NA 67 65 70 63 71 64 69 69 70 64 70 74 69 73 66 67
## [2071] 76 61 68 63 67 66 62 67 66 63 64 67 66 68 NA 68 63 62
## [2089] 72 69 67 65 69 NA 70 91 65 62 65 NA 67 72 60 69 61 70
## [2107] 68 75 75 72 66 71 70 63 72 65 71 65 69 71 68 66 60 68
## [2125] 67 71 74 70 63 64 66 64 69 NA 64 65 69 68 68 68 65 65
## [2143] 66 66 71 68 65 63 66 71 65 68 66 64 70 70 71 70 70 66
## [2161] 64 66 68 61 72 66 68 61 67 66 74 66 67 71 66 71 72 66
## [2179] 62 66 69 69 69 64 68 63 64 69 71 67 66 67 NA 69 NA 66
## [2197] 63 67 66 66 67 66 69 72 60 68 72 64 65 76 59 67 NA 64
## [2215] 67 69 69 67 72 NA 62 69 68 99 70 68 67 66 66 62 72 68
## [2233] 66 68 75 67 65 68 67 67 73 67 71 67 68 68 NA 68 63 68
## [2251] 74 69 70 65 65 68 68 66 70 66 64 70 68 74 71 61 64 64
## [2269] 73 62 71 68 71 72 66 67 66 68 64 66 69 65 72 65 70 64
## [2287] 62 69 62 69 NA NA 64 63 69 68 NA 64 66 71 72 NA 66 65
## [2305] NA 62 68 65 62 74 NA 70 65 66 67 73 65 NA 66 67 58 71
## [2323] 63 73 NA 68 66 78 68 77 65 73 64 67 69 60 66 70 66 64
## [2341] 70 64 72 70 62 66 65 64 NA 71 68 68 65 64 75 61 68 NA
## [2359] 71 66 66 70 62 72 72 63 69 68 67 71 67 62 69 67 87 62
## [2377] 64 74 69 65 66 70 68 70 68 69 66 NA 71 66 61 NA 63 73
## [2395] 68 70 68 68 71 68 70 NA 69 73 72 67 69 68 64 71 68 70
## [2413] 72 65 70 69 64 67 65 62 68 68 68 68 NA 72 69 68 71 69
## [2431] 71 65 68 60 NA 66 66 62 61 69 69 74 62 67 69 66 NA 69
## [2449] 65 72 69 61 63 63 68 68 65 71 64 65 67 67 67 87 67 72
## [2467] 69 65 66 70 71 67 72 63 67 72 72 NA 67 68 70 67 69 74
## [2485] 63 72 71 69 62 NA 68 67 71 70 NA 60 69 71 NA 73 68 67
## [2503] 74 NA 69 69 68 66 69 68 65 71 61 63 66 69 71 73 72 73
## [2521] 65 71 65 67 69 63 68 70 64 64 68 65 66 70 66 69 64 64
## [2539] 69 67 63 67 65 64 68 64 70 70 69 70 65 70 63 74 70 66
## [2557] 68 67 66 66 69 67 69 66 64 61 61 70 65 67 69 63 66 73
## [2575] 68 74 70 68 67 65 66 64 72 70 60 68 71 68 67 70 65 60
## [2593] 65 70 69 64 67 NA 74 67 66 69 64 NA 66 65 67 67 68 65
## [2611] 66 65 71 63 70 70 67 68 63 70 69 66 70 68 70 67 64 62
## [2629] NA 62 66 64 72 NA 65 65 70 68 57 59 64 67 60 67 71 67
## [2647] 69 68 59 75 59 71 71 66 69 65 NA 68 88 66 67 63 68 65
## [2665] 67 67 67 64 65 70 67 68 65 63 72 68 71 70 68 68 68 71
## [2683] 70 67 61 64 67 65 66 62 70 64 70 66 62 63 66 58 70 63
## [2701] 65 NA 73 82 71 73 65 67 67 69 61 64 64 68 62 70 67 70
## [2719] 65 65 70 72 65 71 71 72 64 72 71 66 71 67 69 67 62 67
## [2737] NA NA 69 70 NA 65 66 68 72 65 60 63 73 71 59 70 63 67
## [2755] 65 64 71 NA 63 68 67 66 63 65 66 65 65 63 65 62 66 71
## [2773] 64 67 68 63 64 74 68 68 69 61 69 NA 67 63 68 68 67 69
## [2791] 64 67 70 72 NA 62 67 64 64 70 68 NA 65 59 69 67 68 62
## [2809] 65 69 65 68 68 71 71 66 66 66 65 66 67 66 69 66 64 70
## [2827] NA 67 60 66 72 63 69 NA 69 68 66 63 70 68 68 67 67 69
## [2845] 68 67 70 70 NA 61 68 64 66 73 66 65 68 69 72 63 65 69
## [2863] 62 66 69 67 94 71 66 71 66 60 60 66 67 67 64 66 68 70
## [2881] NA 86 73 61 68 70 71 71 68 70 70 62 67 68 68 64 69 70
## [2899] 73 66 68 68 66 62 67 73 65 70 68 67 66 65 66 66 60 NA
## [2917] 72 68 67 62 69 NA 64 65 75 69 65 60 69 65 67 70 66 69
## [2935] 69 68 70 66 65 65 65 69 69 65 NA 72 67 74 66 66 66 71
## [2953] 66 69 69 68 64 73 66 67 63 61 71 61 62 74 65 NA 66 76
## [2971] 67 71 65 68 68 67 64 60 73 69 70 64 64 65 62 72 64 67
## [2989] 64 61 72 70 70 71 68 68 70 73 69 71 64 NA 69 70 66 65
## [3007] 66 61 71 60 66 61 68 68 65 65 60 67 65 70 64 68 69 NA
## [3025] 65 65 68 66 65 71 68 62 61 70 62 65 68 70 68 69 73 71
## [3043] 63 66 67 66 69 72 NA 67 64 68 71 67 67 64 63 72 63 67
## [3061] 68 64 65 68 66 73 68 72 70 66 66 66 65 71 66 63 58 61
## [3079] 65 67 67 62 86 71 70 71 71 70 67 60 73 NA 62 67 61 61
## [3097] 60 68 65 67 67 74 64 64 67 74 69 62 69 68 74 68 73 70
## [3115] 68 64 71 65 68 67 NA 63 68 66 67 68 72 70 62 69 61 58
## [3133] 63 71 70 64 63 63 71 65 68 70 68 69 70 67 69 67 67 NA
## [3151] 63 67 70 71 74 70 59 64 67 63 66 62 65 73 70 62 NA 96
## [3169] 66 69 70 73 69 71 65 62 65 68 65 67 68 66 62 65 70 68
## [3187] 72 NA 63 67 69 NA 67 69 63 65 58 70 66 63 62 69 66 68
## [3205] 62 64 65 65 65 70 71 65 68 73 64 71 70 68 68 68 59 74
## [3223] 62 64 76 70 69 74 62 70 71 68 66 67 71 74 65 60 69 65
## [3241] 69 70 65 57 68 67 70 68 62 67 66 60 75 67 71 63 67 68
## [3259] 65 72 61 60 72 NA 67 71 66 70 64 66 NA 67 67 64 61 99
## [3277] NA 72 66 64 69 65 66 73 66 65 71 58 69 63 66 69 69 63
## [3295] 65 76 67 70 60 68 68 68 69 62 64 71 68 72 64 73 69 70
## [3313] 69 64 66 69 NA 65 62 75 60 63 66 67 68 72 66 63 71 67
## [3331] NA 66 68 66 68 68 66 66 70 68 65 70 66 68 64 65 NA 66
## [3349] 68 70 65 65 68 67 72 70 72 71 64 69 NA 70 68 71 71 NA
## [3367] 68 70 72 66 65 66 65 72 68 68 67 68 67 NA 65 70 64 66
## [3385] 64 66 67 68 71 67 69 67 61 68 67 64 63 72 69 66 64 61
## [3403] 63 65 71 78 65 66 66 74 62 66 71 67 69 72 72 65 71 64
## [3421] 69 65 69 64 69 68 NA 66 66 67 62 66 68 68 63 66 72 70
## [3439] 63 65 65 66 68 64 66 68 64 62 67 65 59 66 NA 63 68 66
## [3457] NA 66 69 64 68 66 68 62 68 69 70 65 68 67 64 66 67 63
## [3475] 69 70 70 65 NA 67 61 70 68 64 68 68 65 69 63 69 61 69
## [3493] 62 58 71 NA 68 61 67 72 71 67 68 64 73 65 67 63 63 69
## [3511] 68 68 69 73 66 68 65 67 70 64 69 71 68 68 66 70 65 NA
## [3529] 70 67 63 64 60 62 65 69 66 72 68 69 65 65 70 67 73 70
## [3547] 66 68 61 70 66 67 69 64 65 75 63 69 68 66 66 66 68 65
## [3565] 70 68 70 61 64 71 72 66 63 62 66 72 68 NA 70 73 67 65
## [3583] NA 65 70 66 65 68 66 71 65 70 69 67 82 66 66 65 61 72
## [3601] 70 71 84 72 70 62 71 62 68 74 68 NA 65 66 68 67 63 71
## [3619] 63 66 67 66 70 71 68 64 66 72 68 70 64 71 72 71 63 68
## [3637] 63 66 NA NA 70 65 67 66 69 73 66 70 68 65 67 71 70 61
## [3655] 69 63 67 65 63 67 66 72 68 67 NA 66 73 71 65 65 65 68
## [3673] 70 NA 62 66 65 71 61 63 67 70 73 69 61 64 61 63 65 NA
## [3691] 68 72 62 58 68 74 68 67 65 63 71 62 65 66 71 68 72 66
## [3709] 66 67 71 72 64 60 NA 68 62 68 60 72 65 63 66 65 65 67
## [3727] 65 67 66 71 64 61 65 61 69 71 70 62 73 66 66 66 66 65
## [3745] 67 76 66 63 71 63 63 66 72 70 62 69 66 64 NA 67 71 69
## [3763] 70 70 61 NA 67 70 68 69 65 68 67 70 68 69 70 67 70 74
## [3781] 63 72 62 71 68 72 64 64 63 66 71 70 67 73 64 65 62 64
## [3799] 67 74 63 64 64 70 71 63 65 70 65 68 72 67 65 66 67 65
## [3817] 68 68 69 71 64 64 67 70 66 70 70 64 71 63 72 72 63 67
## [3835] 67 64 69 NA 71 70 98 65 63 61 67 64 65 73 69 67 NA 67
## [3853] 66 64 68 66 65 65 67 68 63 70 68 NA NA 69 65 61 65 67
## [3871] 66 69 NA 68 65 64 68 64 70 68 NA 61 66 75 71 69 62 65
## [3889] 61 69 66 64 69 78 68 68 68 69 68 80 NA 64 64 68 65 66
## [3907] 67 64 66 63 71 62 64 72 NA 67 65 63 65 67 67 64 69 60
## [3925] 70 66 66 68 72 64 64 64 72 66 68 95 64 NA 68 67 67 71
## [3943] 63 66 65 68 68 62 67 NA 71 71 61 70 NA 70 67 66 63 65
## [3961] 75 66 61 65 61 73 63 67 62 71 70 70 69 66 72 63 65 71
## [3979] 66 69 62 66 66 64 68 68 67 68 65 NA 85 64 68 NA 65 63
## [3997] 64 62 68 63 68 63 68 62 67 66 65 69 64 75 66 62 70 NA
## [4015] 66 65 68 68 62 66 68 69 67 74 61 64 69 66 61 71 71 69
## [4033] 66 68 71 66 94 68 66 70 68 64 69 59 70 72 64 63 67 62
## [4051] 69 66 66 63 62 58 67 68 67 67 62 66 65 67 69 67 69 62
## [4069] 67 63 66 71 68 67 71 65 64 69 68 67 71 64 NA 69 67 58
## [4087] 66 69 70 70 70 66 61 71 NA 69 74 71 68 69 63 67 NA 66
## [4105] 69 68 63 69 66 71 68 69 65 68 67 65 65 64 69 64 66 65
## [4123] 69 66 64 61 72 67 63 69 70 71 60 70 69 63 69 71 68 64
## [4141] 68 69 65 68 74 72 67 73 68 70 62 67 69 93 68 69 68 64
## [4159] 69 66 68 72 63 NA 65 65 68 70 65 66 66 NA 64 66 63 68
## [4177] 68 65 69 66 72 NA 67 68 71 73 68 69 69 63 62 70 66 62
## [4195] 64 63 71 67 67 67 71 93 72 71 63 65 61 66 61 67 64 69
## [4213] 70 73 63 64 69 69 67 62 66 68 71 66 NA 68 59 70 66 65
## [4231] 66 73 65 65 NA 74 68 65 72 71 69 67 71 68 69 68 73 69
## [4249] 58 65 58 66 NA 67 67 65 71 66 68 65 71 NA 72 69 70 66
## [4267] NA 62 66 70 73 70 71 NA 64 66 82 68 67 68 69 63 66 68
## [4285] 71 69 70 70 NA 68 65 72 67 68 69 70 69 68 65 70 65 61
## [4303] 69 67 65 63 67 76 70 67 66 65 65 63 72 68 62 65 69 61
## [4321] 67 66 70 72 69 68 74 70 67 68 69 66 68 69 66 NA 66 64
## [4339] 63 68 65 65 68 62 67 73 69 65 66 73 72 72 61 69 66 74
## [4357] 66 66 72 70 67 71 63 NA 64 65 65 62 65 64 NA 67 66 NA
## [4375] 68 58 65 68 64 66 92 69 68 63 64 68 67 68 66 68 64 63
## [4393] 62 66 65 66 66 69 67 NA 73 66 61 NA 67 66 69 69 67 65
## [4411] 63 63 66 66 69 72 70 68 66 67 68 62 64 71 65 69 65 71
## [4429] 69 65 66 68 72 74 64 64 63 66 67 64 62 71 63 72 71 61
## [4447] 71 69 61 68 67 70 69 72 66 67 70 68 68 65 63 62 66 62
## [4465] 61 63 64 74 70 68 69 62 71 69 68 65 65 72 63 72 66 71
## [4483] 67 61 70 68 70 65 65 65 65 66 62 63 63 70 67 66 63 66
## [4501] 67 68 67 66 71 69 72 70 68 68 67 62 67 69 64 66 69 70
## [4519] 69 72 61 NA 68 NA 65 66 67 68 67 63 64 66 69 70 72 63
## [4537] 68 67 69 69 71 67 64 68 67 62 68 72 61 67 70 59 70 60
## [4555] 74 68 67 67 63 62 64 68 65 71 68 68 68 67 NA 70 69 70
## [4573] 69 59 64 70 63 66 72 71 62 62 64 65 68 67 61 68 68 62
## [4591] 62 74 68 66 65 66 67 76 66 68 63 65 63 59 74 62 59 71
## [4609] 73 68 68 66 69 70 74 75 71 71 65 NA 65 67 67 71 72 62
## [4627] 70 72 64 66 69 71 68 71 66 68 61 71 70 66 61 67 72 65
## [4645] 68 70 63 69 62 71 64 71 72 66 69 60 68 65 67 66 68 63
## [4663] NA 66 67 66 60 67 NA 70 69 68 67 63 70 71 67 64 66 70
## [4681] 65 68 65 65 69 70 64 62 73 62 62 72 67 68 65 79 66 68
## [4699] 65 67 67 68 72 65 65 70 68 63 68 69 NA 64 69 62 65 70
## [4717] 72 66 70 67 65 68 68 69 72 65 63 68 62 69 65 65 70 59
## [4735] 63 64 63 67 65 64 65 72 72 66 62 68 67 69 67 63 65 71
## [4753] 70 68 65 68 69 NA 62 72 64 58 66 64 68 69 71 71 62 70
## [4771] 63 66 65 69 63 64 66 67 66 65 72 70 67 72 65 62 67 64
## [4789] 72 66 70 66 67 NA 72 68 64 66 68 66 NA 70 69 69 66 68
## [4807] 71 64 67 68 68 69 71 68 65 63 65 72 67 69 67 64 62 71
## [4825] 64 69 65 73 64 64 70 70 64 74 69 67 73 66 67 75 73 67
## [4843] 65 71 63 68 72 NA 67 66 72 64 68 65 74 65 63 65 70 71
## [4861] 66 NA 67 64 67 NA 70 71 68 65 70 67 63 65 70 67 60 65
## [4879] 64 67 71 69 70 69 63 67 66 69 69 72 65 63 69 69 64 69
## [4897] 72 62 66 65 65 67 63 66 61 64 65 68 69 61 72 61 66 60
## [4915] 69 72 69 71 64 71 64 67 67 66 73 73 70 70 62 68 65 73
## [4933] 66 64 63 62 70 NA 64 70 62 67 66 74 69 70 68 71 73 69
## [4951] 61 68 66 67 64 67 61 62 69 61 69 64 65 64 68 67 68 61
## [4969] 69 64 74 66 68 65 66 66 65 67 65 63 67 70 68 66 NA 72
## [4987] 68 66 62 67 62 67 68 66 68 62 68 62 69 62 71 69 66 64
## [5005] 65 NA 69 68 71 66 65 72 67 67 70 64 65 68 67 66 69 64
## [5023] 68 68 65 65 65 67 63 62 73 72 71 67 66 68 70 66 56 71
## [5041] 64 NA 70 70 71 70 62 72 62 67 NA 60 72 66 66 69 70 70
## [5059] 70 67 67 59 68 71 61 63 67 70 69 66 70 67 61 74 70 66
## [5077] 73 65 64 63 69 NA 65 NA 69 71 68 70 71 68 69 71 63 66
## [5095] 67 71 59 66 72 70 68 63 69 75 67 74 66 65 60 63 69 68
## [5113] 65 74 65 61 67 66 69 65 65 66 73 64 67 67 68 71 64 67
## [5131] 68 67 70 64 63 71 64 70 70 67 62 NA 69 NA 70 69 65 66
## [5149] 69 66 65 66 72 62 64 61 70 67 66 66 68 67 65 70 68 61
## [5167] 65 71 66 61 67 66 71 62 67 64 68 67 63 70 67 71 62 75
## [5185] 72 73 64 66 69 70 70 71 64 71 63 68 71 66 72 65 60 67
## [5203] 65 64 72 62 67 67 69 65 62 69 72 63 64 67 70 64 69 72
## [5221] 69 75 67 67 64 68 65 70 57 69 70 63 66 64 62 71 64 72
## [5239] 64 71 68 68 68 69 67 66 65 63 62 67 65 66 64 67 67 61
## [5257] 66 66 67 64 67 68 64 63 68 64 70 64 59 71 67 73 66 73
## [5275] 62 69 66 NA 65 67 64 67 66 NA 68 64 63 72 75 71 66 71
## [5293] NA NA 58 62 69 65 69 68 70 72 66 68 67 61 64 74 64 64
## [5311] 61 71 72 68 69 74 70 69 64 71 65 71 66 64 NA 71 65 59
## [5329] 63 64 63 70 70 NA 65 71 70 66 64 64 59 65 NA 67 62 70
## [5347] 75 66 65 64 70 71 68 64 67 65 62 68 66 68 NA 68 66 70
## [5365] 60 69 65 NA 64 71 66 66 68 NA 66 61 70 68 65 69 67 62
## [5383] 61 65 65 66 NA 69 70 63 64 65 71 61 69 69 66 72 60 62
## [5401] 66 69 69 71 57 72 66 70 67 65 68 63 63 68 60 67 65 68
## [5419] 62 65 66 67 60 74 62 61 NA 66 NA 72 70 71 64 70 68 61
## [5437] 68 64 64 NA 72 66 74 65 64 69 62 62 72 73 64 65 70 66
## [5455] 70 69 64 63 66 68 97 71 66 72 70 69 66 69 65 75 70 70
## [5473] 69 73 74 66 74 67 67 70 67 80 70 71 64 68 68 69 72 65
## [5491] 64 64 58 69 61 68 66 68 70 62 71 61 NA 65 63 74 68 65
## [5509] 66 69 69 70 70 71 72 61 68 66 70 NA 62 69 69 64 63 69
## [5527] 61 70 64 76 73 69 72 70 73 68 66 67 67 62 72 65 69 69
## [5545] 69 69 69 70 67 69 75 66 63 64 66 72 71 70 67 65 65 73
## [5563] 66 NA 71 66 65 75 74 65 71 65 65 67 66 67 66 65 59 63
## [5581] 65 61 68 65 72 59 63 69 70 67 66 68 71 69 66 66 74 66
## [5599] 72 69 68 71 61 65 71 59 71 72 71 67 67 74 63 68 NA 66
## [5617] 67 70 65 68 70 66 69 65 68 65 70 NA NA 64 70 64 67 68
## [5635] 67 66 66 67 NA NA 68 67 69 64 67 67 67 67 68 65 70 68
## [5653] 72 67 66 68 75 66 67 71 68 65 67 66 60 NA 64 72 60 NA
## [5671] 62 70 65 77 71 66 74 70 NA 64 NA 68 63 61 61 65 69 69
## [5689] 65 72 69 71 67 72 70 68 66 68 71 70 65 65 68 69 66 62
## [5707] 70 65 71 68 65 70 69 66 67 63 70 65 70 74 68 64 73 66
## [5725] 66 67 67 69 69 68 64 70 67 68 67 73 65 69 63 68 64 68
## [5743] 66 65 69 69 74 64 63 64 71 NA 72 67 64 70 65 69 65 66
## [5761] 67 68 65 68 63 65 61 68 65 66 65 NA 70 70 67 75 65 66
## [5779] 62 64 60 70 72 67 67 72 63 60 NA 72 70 71 66 NA 73 71
## [5797] 64 66 69 66 63 62 98 71 66 75 68 69 68 60 64 71 69 60
## [5815] 70 66 68 67 69 75 65 65 66 64 70 63 66 71 68 68 71 63
## [5833] NA 73 68 70 66 72 70 68 60 68 74 68 72 69 98 68 70 64
## [5851] 65 67 65 70 68 65 74 65 68 74 67 64 66 61 73 70 70 63
## [5869] 69 NA 68 65 68 69 66 58 67 65 62 65 69 70 70 63 69 64
## [5887] 69 70 64 65 70 60 68 61 68 61 64 66 70 65 74 66 65 69
## [5905] 69 66 63 69 65 67 67 65 69 NA 67 66 64 70 65 65 64 64
## [5923] 61 65 68 70 74 60 71 70 67 68 64 67 65 72 65 71 72 70
## [5941] 63 67 67 62 72 69 61 67 66 68 62 63 70 68 71 65 59 64
## [5959] 67 68 95 70 68 65 NA 67 69 68 72 71 75 70 66 67 70 71
## [5977] 64 65 64 62 64 66 64 71 NA 70 71 68 66 66 65 64 67 65
## [5995] 69 69 69 68 67 68 65 69 73 76 69 69 68 70 NA 73 64 65
## [6013] 62 64 69 67 65 63 66 70 70 67 65 66 66 72 64 71 70 64
## [6031] 70 67 NA 68 69 68 68 64as.numeric(czynniki4$Sleep_Hours)## [1] 7 8 7 8 6 8 NA 6 6 8 6 8 8 NA 8 10 6 9 7 5 6 8 8 5
## [25] 6 6 4 4 7 8 5 6 7 9 8 6 8 6 7 7 9 8 6 6 7 5 7 8
## [49] 8 7 5 5 6 8 8 7 10 9 8 8 NA 4 5 7 7 7 7 4 8 7 7 8
## [73] 7 7 6 4 5 7 7 7 6 5 7 7 8 6 4 4 6 7 7 6 5 4 NA 7
## [97] 6 5 6 7 7 7 9 6 9 7 7 8 6 7 5 8 8 9 9 6 8 6 7 10
## [121] 8 8 6 7 NA 9 7 NA 5 9 6 8 6 8 NA 9 8 6 8 8 5 5 5 5
## [145] 8 8 4 6 5 8 6 5 7 8 6 7 6 9 6 6 7 7 8 9 9 6 7 NA
## [169] 9 6 8 8 8 9 NA 6 8 7 4 5 8 8 5 9 7 5 6 NA 6 4 7 8
## [193] 5 7 6 8 4 8 4 7 6 NA 5 9 5 5 10 7 5 7 4 6 7 9 7 7
## [217] 6 9 8 8 7 5 9 7 7 8 7 5 7 7 9 4 7 8 NA 6 5 6 9 4
## [241] 5 6 6 7 9 5 7 7 6 5 6 6 8 8 5 6 6 10 7 5 6 6 8 7
## [265] 7 7 7 4 7 5 10 7 7 6 8 5 7 6 8 6 9 8 8 9 6 8 4 7
## [289] 6 5 6 6 7 6 7 6 6 7 7 8 8 8 7 7 8 6 4 5 9 7 7 7
## [313] 8 NA 7 8 6 8 NA 7 6 7 6 9 4 8 8 6 8 7 5 9 8 8 6 8
## [337] 5 4 5 NA 6 6 6 4 7 NA 6 9 7 8 NA 8 7 5 6 7 4 NA 10 8
## [361] 8 7 8 9 8 7 7 8 6 8 6 5 6 10 6 NA 6 7 4 5 6 5 7 5
## [385] 7 NA 7 6 9 8 NA 6 8 9 8 5 NA 8 7 6 7 7 NA 8 6 7 9 7
## [409] 8 5 8 8 6 7 7 8 6 7 9 9 8 NA 9 7 7 6 8 8 7 5 8 6
## [433] 7 9 5 7 NA 7 7 8 7 8 7 7 NA 7 6 8 7 6 9 7 5 7 7 7
## [457] 6 NA 10 4 5 6 6 5 6 7 5 8 5 8 8 6 5 8 6 NA 8 6 7 6
## [481] 9 6 7 8 7 8 7 5 7 NA 7 9 4 8 6 6 9 7 6 8 NA 9 10 8
## [505] 7 5 9 NA 8 8 7 NA 10 7 6 9 7 7 9 8 8 NA 5 6 7 7 8 8
## [529] 5 10 7 9 4 7 5 6 7 6 9 10 6 NA 5 9 7 7 7 8 5 7 6 7
## [553] 8 6 9 4 9 9 6 6 5 8 7 5 NA 6 7 7 6 6 8 NA 9 6 4 6
## [577] 6 5 7 7 4 7 9 8 7 4 6 9 6 6 5 7 7 6 10 8 7 4 8 10
## [601] 7 6 5 8 9 6 6 7 6 5 6 6 9 9 8 NA 6 9 8 5 6 5 4 NA
## [625] 5 6 6 9 5 5 8 6 6 5 8 7 7 6 6 7 8 9 9 8 8 6 8 7
## [649] 8 8 8 5 7 6 6 NA 7 4 8 9 8 7 9 6 7 10 5 5 8 7 6 5
## [673] 4 5 9 7 4 9 9 9 6 7 7 8 9 7 8 7 7 6 5 6 6 NA 9 7
## [697] 6 8 7 8 6 9 9 7 8 9 6 7 7 5 8 9 7 8 9 6 6 6 8 8
## [721] 7 8 9 8 7 7 8 7 8 9 7 4 10 7 9 10 9 7 10 9 NA 6 4 8
## [745] 9 8 4 5 10 7 9 5 7 7 6 10 7 5 5 8 6 6 8 4 6 5 6 7
## [769] 7 7 9 7 NA 10 7 10 7 7 NA 7 9 10 4 NA 6 4 8 8 8 8 7 8
## [793] 7 7 7 5 8 5 NA 7 5 6 6 9 7 8 9 9 7 6 8 NA 8 7 8 7
## [817] 6 8 7 10 6 8 6 4 8 6 9 8 7 5 8 6 5 8 5 4 9 6 4 6
## [841] 6 9 5 5 8 6 NA 6 NA NA 7 9 6 6 8 9 6 7 8 9 8 6 10 NA
## [865] 7 8 8 10 7 7 9 7 NA 8 8 4 4 NA 7 7 7 8 8 8 NA 7 7 9
## [889] 6 7 7 9 4 7 8 10 7 6 10 8 9 8 5 5 8 8 6 9 6 7 7 9
## [913] 5 6 5 10 7 6 NA 8 8 6 5 7 9 NA 6 5 8 10 8 6 6 10 6 7
## [937] 7 8 9 9 7 7 8 6 NA 7 8 10 8 7 6 7 5 4 8 8 NA 7 4 8
## [961] 9 8 7 NA 6 7 7 6 7 NA 10 7 6 NA 9 9 10 7 8 5 6 5 8 7
## [985] 7 6 4 7 7 4 8 7 8 10 7 8 9 8 6 5 8 6 9 6 7 5 6 6
## [1009] 6 7 6 10 NA 9 7 7 6 10 7 6 NA NA 9 6 6 9 10 7 9 5 6 NA
## [1033] 8 7 9 6 7 5 9 9 8 7 6 7 8 NA 9 9 6 7 6 6 9 7 7 7
## [1057] 7 6 NA 6 6 7 NA 6 8 7 7 8 4 6 8 7 7 6 9 8 NA 9 6 8
## [1081] 8 7 7 9 6 9 6 7 6 10 7 5 7 8 7 6 9 5 6 7 6 8 10 6
## [1105] 9 5 8 6 8 4 5 8 6 7 10 NA 8 6 7 5 6 7 7 8 8 5 6 4
## [1129] 6 8 9 7 9 8 7 6 4 9 NA 9 NA 7 6 7 7 7 6 6 9 6 4 5
## [1153] NA 7 6 9 8 10 6 7 9 8 6 8 8 6 7 9 8 6 6 8 4 6 9 7
## [1177] 6 5 8 7 7 8 7 7 5 5 8 8 8 6 8 6 NA 6 6 NA 8 7 7 6
## [1201] 7 7 6 7 7 10 6 6 7 6 5 5 6 6 7 4 8 6 8 8 6 NA 9 5
## [1225] 8 NA 9 6 6 NA 8 6 7 6 5 7 6 6 9 6 NA 9 6 7 8 8 10 6
## [1249] 5 8 7 7 6 6 NA 6 7 NA 5 5 6 9 6 5 6 5 8 5 NA 7 8 8
## [1273] 5 9 7 10 9 7 10 7 10 8 8 NA NA 8 7 7 NA 8 8 6 7 4 8 10
## [1297] 7 5 8 6 8 8 NA 7 8 7 6 8 5 7 5 6 6 9 9 9 6 8 7 7
## [1321] 4 8 7 8 8 6 7 5 9 8 6 8 7 6 7 8 8 10 7 NA 8 7 6 6
## [1345] 4 8 5 6 7 10 5 10 9 8 9 8 4 6 7 6 8 7 8 7 7 6 5 7
## [1369] 6 9 5 10 7 NA 6 8 7 7 8 9 6 7 7 10 7 8 8 8 6 6 7 4
## [1393] 7 6 7 7 5 NA 8 7 8 5 9 8 7 NA 9 6 5 6 7 7 9 6 6 5
## [1417] 8 5 8 6 6 10 9 7 5 10 7 7 8 4 7 7 5 7 7 10 9 7 7 9
## [1441] 7 5 10 6 10 8 6 NA 8 5 8 10 5 6 9 7 7 9 8 6 10 5 7 6
## [1465] NA 5 7 8 9 9 7 6 9 6 5 8 9 6 8 8 6 9 5 6 6 5 8 8
## [1489] 8 7 8 7 6 6 4 9 9 10 6 6 NA 8 9 6 8 9 8 5 7 4 5 5
## [1513] 7 7 7 5 7 8 8 8 8 8 8 5 5 6 NA 7 7 4 7 7 4 7 5 6
## [1537] 8 7 6 6 6 7 5 9 5 8 6 7 8 6 7 8 9 6 6 8 7 7 9 4
## [1561] 5 4 9 8 5 7 NA 4 7 5 8 5 7 9 8 8 7 5 6 7 7 5 8 5
## [1585] 9 7 8 8 10 7 6 9 5 7 7 8 5 7 7 5 7 7 6 6 5 8 9 10
## [1609] 8 6 6 7 7 7 9 6 9 7 6 6 7 8 6 8 6 7 5 8 NA 9 8 7
## [1633] 9 8 9 6 8 9 5 5 4 5 6 8 7 6 5 7 8 8 10 NA 7 7 7 6
## [1657] 4 5 8 7 8 8 8 8 7 7 4 6 6 7 6 8 6 NA 6 6 6 6 9 7
## [1681] 7 6 7 7 7 9 7 5 7 6 8 7 9 6 7 5 7 5 7 7 7 8 7 5
## [1705] 6 7 7 7 9 7 8 4 NA 10 9 NA 10 7 7 7 NA 4 8 7 7 7 9 8
## [1729] 7 7 6 7 8 7 7 8 5 6 5 7 8 9 9 6 7 6 9 9 7 6 4 5
## [1753] 5 10 5 6 10 7 8 7 4 9 8 7 10 6 7 NA NA 8 7 5 6 5 9 5
## [1777] 9 9 6 6 6 9 9 6 9 9 7 7 9 9 8 7 9 10 6 7 8 8 6 9
## [1801] 6 6 6 5 8 7 9 8 4 9 10 9 9 NA 6 7 8 8 6 6 5 8 6 7
## [1825] 10 8 7 8 9 5 6 7 6 7 5 8 6 NA 7 8 4 8 7 8 5 8 9 7
## [1849] 6 6 8 8 8 7 NA 7 6 8 7 9 9 7 8 6 7 8 5 8 6 6 6 7
## [1873] 5 7 7 6 5 8 5 10 8 8 7 6 6 5 7 9 5 9 NA 8 8 7 7 6
## [1897] 7 7 NA 8 7 7 6 6 8 6 6 6 6 9 7 7 7 5 9 8 8 8 10 6
## [1921] 5 8 5 7 7 8 6 6 8 6 7 9 7 9 7 6 8 4 8 6 8 7 5 6
## [1945] 7 7 8 8 8 8 NA 10 8 8 10 7 6 9 9 7 10 7 8 9 7 9 6 6
## [1969] 9 7 6 7 8 5 8 8 9 7 7 7 7 10 5 8 7 7 8 9 8 9 7 7
## [1993] 5 10 7 8 9 6 9 7 9 8 7 5 8 4 8 7 4 6 6 NA 9 9 6 6
## [2017] NA 7 6 6 6 6 9 8 8 9 8 9 8 7 8 7 5 4 10 6 6 9 5 8
## [2041] 10 10 6 7 6 7 9 5 8 7 9 9 6 7 8 8 4 8 9 7 8 9 7 8
## [2065] 7 7 6 7 10 6 NA 7 9 9 6 6 6 6 NA 6 6 NA 7 7 6 5 9 7
## [2089] 10 8 10 8 7 6 6 9 7 8 8 8 6 9 7 7 8 7 4 9 9 4 5 10
## [2113] 7 7 6 5 7 8 7 8 NA 6 7 9 6 7 10 6 9 7 10 5 7 5 6 6
## [2137] 7 5 NA 8 5 6 10 7 4 5 7 7 NA 10 10 7 8 8 9 6 8 7 7 7
## [2161] 5 4 7 6 8 8 7 9 7 5 7 9 4 7 8 10 9 7 8 4 5 7 7 7
## [2185] 7 7 5 7 5 6 7 8 7 6 5 6 7 8 8 5 8 5 8 8 4 8 NA 9
## [2209] 6 7 8 8 8 6 8 8 7 6 6 9 8 7 7 4 7 5 7 9 NA 7 8 6
## [2233] 7 8 NA 7 9 8 5 5 4 5 7 9 6 8 4 NA 6 10 4 4 6 4 6 7
## [2257] 7 5 9 8 8 5 9 9 7 8 7 NA 7 6 7 9 6 6 NA 7 8 8 7 10
## [2281] 7 8 10 8 6 7 7 NA 6 9 8 7 NA 7 8 10 4 8 7 7 4 8 7 6
## [2305] 7 7 4 7 8 6 7 9 7 8 7 10 6 6 7 6 5 8 NA 6 5 4 8 5
## [2329] 7 8 8 5 NA 9 6 6 8 5 7 8 5 6 9 7 8 8 7 5 6 7 5 5
## [2353] 9 NA NA 8 6 4 6 7 7 7 7 6 8 5 8 6 10 7 6 6 6 8 8 8
## [2377] 7 8 9 8 7 8 5 10 8 8 7 4 7 7 6 6 8 9 7 6 7 7 8 6
## [2401] 8 8 6 4 6 9 4 9 4 6 6 NA 7 7 6 8 NA 7 6 8 8 6 6 6
## [2425] 7 8 7 4 8 5 6 7 7 8 6 6 7 NA 8 7 9 9 8 5 8 7 6 6
## [2449] 7 6 7 7 8 7 6 4 8 7 7 9 5 7 NA 8 4 NA 8 6 7 6 NA 8
## [2473] 5 5 9 10 8 8 7 7 7 9 7 7 7 9 7 7 6 5 9 9 9 5 9 10
## [2497] 9 9 8 8 5 6 7 7 8 4 7 8 8 8 8 8 7 6 NA 8 10 8 8 5
## [2521] 7 7 8 8 8 10 NA 8 8 10 8 8 8 9 6 10 4 7 7 7 9 8 6 6
## [2545] 7 9 7 7 8 7 9 7 7 NA 8 7 NA 10 8 NA 7 7 8 4 4 9 7 6
## [2569] 5 7 7 9 8 7 8 9 8 8 7 6 5 5 8 8 9 8 9 7 NA 5 7 4
## [2593] 7 9 7 8 7 6 7 9 8 6 5 7 6 7 5 9 7 7 6 7 7 6 7 9
## [2617] 4 7 6 9 7 5 7 8 10 4 9 5 7 NA 7 7 9 8 7 7 8 9 8 9
## [2641] 6 9 8 6 7 7 7 NA 6 7 6 6 9 7 10 7 9 7 7 8 NA 7 7 6
## [2665] 7 8 7 7 7 7 8 7 7 8 7 7 7 5 7 10 6 6 10 NA 9 7 7 8
## [2689] 7 NA 4 NA NA 10 8 NA 9 6 6 4 6 8 9 5 7 4 7 10 4 NA 8 8
## [2713] 6 9 6 8 9 8 8 8 9 7 6 7 6 6 9 8 8 9 8 10 4 6 7 7
## [2737] 10 8 6 8 4 7 7 6 7 6 6 8 8 6 6 6 7 6 9 7 8 5 6 8
## [2761] 8 5 7 7 6 8 5 6 8 7 7 7 8 8 8 7 6 6 5 6 6 9 5 9
## [2785] 7 7 8 5 6 5 6 NA 9 6 4 6 8 9 7 6 7 8 5 7 7 7 7 6
## [2809] 8 7 7 5 8 6 9 5 4 4 4 8 7 9 7 7 7 6 6 5 8 7 7 10
## [2833] 6 7 7 9 7 7 10 6 7 8 6 8 6 NA 8 7 5 NA 7 8 7 8 8 7
## [2857] 7 7 6 NA 8 9 6 8 9 9 5 NA 4 5 9 6 5 9 5 9 5 5 7 6
## [2881] 7 10 7 9 7 NA 4 8 8 6 10 6 5 8 5 7 8 NA 6 9 5 8 8 7
## [2905] 7 6 6 7 8 9 4 4 9 7 7 7 10 8 6 6 NA NA 9 6 5 9 5 8
## [2929] 6 9 5 6 8 8 9 8 8 9 5 6 5 4 8 9 8 8 7 7 10 9 6 9
## [2953] 9 8 8 5 5 5 NA 6 8 8 8 6 7 8 8 6 7 7 6 NA 6 7 6 6
## [2977] 8 6 NA 8 7 7 7 8 7 7 5 7 9 6 5 8 8 6 7 7 NA 8 6 8
## [3001] 6 9 10 6 8 7 8 6 7 6 7 5 7 5 NA 7 8 8 8 5 9 6 6 7
## [3025] 8 8 6 7 7 8 6 6 5 NA 8 9 NA 4 7 10 6 7 5 7 7 5 5 5
## [3049] 6 8 6 9 6 7 8 9 6 8 6 10 5 8 9 5 8 6 10 4 5 5 5 NA
## [3073] 10 9 7 6 8 7 6 5 7 7 6 6 8 8 10 NA 5 7 5 NA 10 9 9 9
## [3097] 4 8 6 8 10 9 7 9 4 8 8 8 8 8 4 7 6 8 6 NA 5 7 7 8
## [3121] 7 9 7 NA 7 NA 5 5 9 6 7 7 NA 9 7 6 6 8 8 8 7 5 8 7
## [3145] 7 5 6 8 7 8 9 8 8 6 6 9 6 8 10 8 7 5 7 9 7 9 8 7
## [3169] 5 6 6 8 7 9 7 6 6 7 6 9 7 6 5 7 8 6 7 8 7 5 5 4
## [3193] 8 5 7 6 6 6 6 9 6 8 9 NA 8 6 7 6 7 5 8 5 7 6 8 7
## [3217] 5 8 7 7 10 9 7 5 5 9 6 5 8 9 9 6 8 7 8 7 6 9 7 6
## [3241] 7 6 8 7 6 10 5 8 7 5 6 5 7 7 10 6 9 8 4 6 8 NA 6 6
## [3265] 7 10 6 7 8 5 5 5 5 9 8 8 8 7 7 NA 5 10 NA 6 7 10 9 8
## [3289] 8 6 8 7 NA 9 7 5 6 8 9 8 8 7 7 7 7 6 8 NA 5 6 8 8
## [3313] 4 8 7 6 7 5 7 5 6 6 8 NA 8 NA 7 8 9 5 6 8 9 7 5 7
## [3337] 8 7 5 9 6 8 4 NA 6 8 5 7 9 6 9 8 9 7 7 10 8 7 8 6
## [3361] 7 9 7 6 6 7 6 5 5 9 7 7 6 6 6 7 5 9 7 7 8 8 6 8
## [3385] 8 7 9 8 NA 9 7 7 8 7 8 6 4 8 5 NA 8 NA 4 7 7 8 5 NA
## [3409] 8 6 10 6 7 5 7 4 7 9 5 5 9 5 10 8 9 6 9 NA 8 6 5 7
## [3433] 7 6 9 10 7 6 10 8 8 9 7 7 9 8 6 6 9 9 10 6 7 6 NA 7
## [3457] 8 6 4 5 7 10 6 7 8 6 6 7 6 4 6 9 9 6 6 6 7 6 7 NA
## [3481] 8 6 6 8 8 7 8 10 8 10 7 9 9 7 6 6 8 5 6 8 4 5 10 9
## [3505] 6 5 5 8 10 10 5 7 6 NA 5 6 6 8 6 8 9 10 8 7 9 9 8 5
## [3529] 9 8 6 6 8 4 7 6 6 5 9 4 7 6 10 7 4 8 5 8 8 9 7 8
## [3553] 7 6 9 5 7 6 8 NA 6 7 9 6 6 5 6 7 7 10 4 10 9 7 6 7
## [3577] 10 6 7 6 6 6 5 7 7 6 4 7 7 7 8 6 9 8 8 10 6 9 9 7
## [3601] 10 7 7 7 8 NA 10 6 4 10 9 8 6 8 5 7 7 8 5 NA 7 8 7 6
## [3625] 4 5 6 5 8 7 10 10 9 6 9 4 9 4 7 9 8 5 7 8 7 6 8 NA
## [3649] 7 9 NA 6 9 9 6 6 10 7 7 7 9 10 7 10 6 7 8 6 NA 6 5 4
## [3673] 7 8 5 7 7 7 6 7 7 8 5 5 7 6 7 6 9 9 8 8 7 7 10 6
## [3697] 5 NA 5 5 7 8 5 6 8 6 6 5 6 6 7 8 7 7 8 6 8 5 7 9
## [3721] 7 9 7 10 4 8 4 7 9 9 8 7 8 10 8 6 8 6 8 8 8 7 9 6
## [3745] 7 7 9 6 7 6 8 5 9 8 6 6 9 8 6 6 8 8 8 7 8 7 6 9
## [3769] NA 7 7 6 7 6 8 7 5 7 6 4 7 9 7 8 7 6 6 5 8 8 7 4
## [3793] 8 6 7 5 7 7 4 9 7 7 8 NA 8 5 4 7 9 5 6 4 7 8 8 6
## [3817] 4 5 9 8 NA 5 9 6 8 5 7 9 6 8 5 6 8 NA 8 6 5 6 9 6
## [3841] 9 7 10 10 9 5 4 7 8 8 6 5 8 10 6 10 7 7 8 7 9 6 7 5
## [3865] NA 5 8 5 8 6 10 9 8 5 NA 6 6 9 6 6 6 8 5 7 8 4 5 7
## [3889] 9 9 6 9 7 7 7 6 6 5 8 8 8 5 6 9 7 7 8 7 NA 8 5 9
## [3913] 6 8 7 6 NA 8 7 10 8 NA 9 8 9 6 NA 7 9 10 6 7 8 7 6 6
## [3937] 8 7 7 7 6 7 6 6 5 7 8 9 5 9 7 5 6 4 5 10 6 8 7 7
## [3961] 8 4 9 7 6 8 7 7 8 7 5 8 7 4 NA 6 8 6 5 9 8 7 8 8
## [3985] 5 7 9 7 8 7 9 9 9 10 8 8 6 6 7 5 7 8 5 7 7 7 8 8
## [4009] 9 8 9 7 7 7 9 7 7 10 5 8 7 7 6 6 6 8 8 4 5 8 8 5
## [4033] NA 8 6 5 7 7 7 6 10 6 6 7 NA 8 9 8 4 NA 9 9 8 6 7 6
## [4057] 5 NA 10 6 9 6 5 8 7 9 9 7 9 6 9 5 9 9 6 9 5 6 7 8
## [4081] 5 10 4 7 4 9 6 7 7 5 5 9 7 4 7 4 7 6 7 8 9 5 6 8
## [4105] 7 4 7 9 5 7 4 8 7 6 6 5 9 6 8 6 NA 9 10 10 6 6 10 7
## [4129] NA 6 6 8 4 8 8 6 7 7 7 8 6 10 7 7 10 4 10 7 6 5 6 7
## [4153] 8 7 6 9 10 9 6 8 8 NA 6 6 9 8 5 8 10 6 6 8 9 7 9 6
## [4177] 5 6 5 8 6 7 NA 7 7 9 5 8 8 7 6 5 10 7 7 10 7 10 5 NA
## [4201] 5 7 6 7 6 7 6 9 5 7 5 6 7 7 5 6 5 9 5 10 9 8 7 8
## [4225] 8 9 7 9 7 10 7 5 7 8 NA 4 8 8 5 7 7 8 6 6 5 10 8 6
## [4249] 5 5 7 4 8 8 7 7 8 7 8 5 8 7 9 7 7 6 9 4 8 7 7 7
## [4273] 8 6 7 8 6 8 8 6 5 6 7 7 9 6 6 8 6 6 6 4 8 8 NA 10
## [4297] 9 6 9 7 6 6 NA 7 9 NA 6 5 8 8 9 7 8 8 7 8 8 7 10 10
## [4321] 7 7 NA 7 9 5 7 8 9 5 6 6 5 7 NA 7 5 4 8 6 5 8 6 4
## [4345] 7 9 6 6 10 8 10 7 7 9 7 7 10 7 8 6 8 7 8 7 8 5 9 6
## [4369] NA 6 7 7 8 8 8 8 7 7 8 5 4 NA 7 8 6 9 8 NA 4 NA 9 7
## [4393] 7 7 NA 9 6 8 7 8 6 9 8 NA 5 5 10 NA 6 8 6 4 4 7 9 9
## [4417] 9 8 NA 9 4 8 5 6 8 8 6 8 8 7 7 10 7 7 NA 7 8 9 7 6
## [4441] 10 4 10 9 9 9 10 NA 6 6 NA 6 5 6 7 9 NA 8 5 4 NA 6 NA 6
## [4465] 6 6 5 4 4 7 9 7 7 5 6 NA 4 9 4 7 8 9 6 10 7 7 7 10
## [4489] NA 6 9 8 5 5 7 8 6 4 5 9 8 9 9 6 6 7 8 9 10 NA 8 10
## [4513] 7 9 8 NA 7 5 8 8 6 7 6 6 6 5 6 8 9 10 6 9 8 7 8 NA
## [4537] NA 6 6 6 6 7 7 6 10 6 7 4 7 5 6 4 6 NA 7 6 7 6 7 7
## [4561] 7 NA 8 8 7 7 7 7 7 6 4 7 8 5 NA 8 NA 7 9 9 6 8 6 10
## [4585] 7 5 8 9 9 7 8 6 8 8 5 7 7 7 7 9 NA 4 10 4 8 5 9 7
## [4609] 8 4 8 8 8 8 7 7 6 6 NA 6 4 6 7 8 4 4 7 9 4 8 9 NA
## [4633] 8 7 10 6 7 6 7 7 9 9 8 9 6 6 8 7 10 4 8 6 6 5 9 NA
## [4657] 6 6 5 5 6 9 10 6 6 5 8 8 7 6 9 8 8 NA 7 6 8 8 8 5
## [4681] 8 7 6 8 7 8 7 7 9 5 6 6 7 6 6 7 9 NA 8 NA 6 4 8 8
## [4705] 7 6 6 8 8 8 8 8 8 6 5 7 8 5 7 9 NA 9 7 NA 6 7 5 5
## [4729] NA 7 10 7 7 9 6 4 6 6 4 7 6 5 8 7 7 8 7 NA 6 5 7 6
## [4753] 8 7 8 6 5 10 7 8 NA 7 9 5 10 7 6 6 7 8 7 8 8 7 6 7
## [4777] 10 7 9 6 7 NA NA 5 9 10 6 6 7 6 5 9 6 7 5 8 7 4 9 8
## [4801] 7 7 10 8 7 5 7 8 7 6 6 8 6 4 NA 7 8 8 5 7 6 6 6 7
## [4825] 10 6 7 7 7 NA 7 6 9 5 8 6 4 6 6 5 8 5 6 7 6 6 6 6
## [4849] 8 6 7 9 8 5 8 9 6 5 6 7 8 6 4 5 8 10 7 9 5 6 4 6
## [4873] 8 6 10 10 4 6 8 5 9 9 5 7 7 8 7 8 5 9 9 7 NA NA 7 NA
## [4897] 7 7 5 5 10 7 7 9 8 8 5 7 6 6 7 8 7 9 9 9 7 6 7 9
## [4921] 9 4 7 4 7 6 6 8 6 7 6 7 6 8 7 7 6 8 8 7 7 8 8 7
## [4945] 9 8 10 8 9 9 7 5 9 6 7 10 5 6 6 7 8 8 NA 6 5 6 8 7
## [4969] 4 4 7 8 6 8 5 7 7 8 5 5 NA 5 NA 9 NA 8 8 8 7 10 7 8
## [4993] 6 6 9 6 8 8 7 4 9 6 7 5 6 6 7 6 10 7 8 8 6 6 6 8
## [5017] 8 7 7 10 7 4 8 8 9 8 6 NA 7 9 9 NA 8 9 7 10 9 6 7 8
## [5041] 10 8 7 9 7 6 8 6 10 NA 8 9 7 7 7 5 7 8 5 9 7 7 5 6
## [5065] 5 6 7 8 4 7 7 6 6 9 10 4 6 7 8 7 7 8 8 8 7 7 8 7
## [5089] 8 6 8 9 5 5 8 7 NA 8 6 8 8 6 9 7 5 5 8 5 5 8 5 8
## [5113] 8 4 8 5 6 9 6 7 6 6 5 7 7 8 7 NA 8 6 5 8 6 7 6 6
## [5137] 4 8 4 9 9 6 NA 10 7 7 9 5 7 8 8 7 7 7 8 7 7 6 10 6
## [5161] 8 10 5 8 10 6 6 7 6 10 7 6 6 8 8 NA 5 7 7 6 9 8 7 6
## [5185] 10 5 6 7 8 5 6 8 NA 6 7 6 7 7 9 8 7 7 10 6 7 6 8 10
## [5209] 7 7 7 5 7 10 8 9 9 6 10 4 7 4 4 8 9 4 7 9 10 NA 5 5
## [5233] 7 10 6 NA 5 7 NA 7 8 8 7 7 7 7 6 5 7 6 NA 7 8 5 10 4
## [5257] 9 7 6 5 7 7 9 7 7 8 7 7 7 8 6 6 8 5 7 6 8 9 6 8
## [5281] 7 6 7 9 7 9 7 5 7 7 6 10 9 7 9 NA 5 8 8 6 6 8 4 8
## [5305] 7 NA 8 6 5 9 7 7 8 6 8 8 9 9 7 8 NA 7 7 4 9 8 7 7
## [5329] 6 6 8 5 5 8 7 7 7 10 7 7 10 7 10 NA 5 10 6 8 10 9 6 8
## [5353] 8 6 8 6 7 5 NA 7 5 8 8 8 9 8 7 7 10 8 7 7 NA 5 10 8
## [5377] 5 7 9 6 6 NA 8 6 8 NA 6 7 8 6 8 9 6 10 9 7 NA 6 NA 7
## [5401] 5 4 7 7 6 5 4 6 8 7 8 8 8 5 6 10 4 7 8 4 6 10 7 6
## [5425] NA 6 10 6 6 5 7 7 9 NA 8 7 4 6 6 10 8 7 4 4 8 8 6 7
## [5449] 7 7 6 8 9 6 5 7 8 8 8 8 7 7 8 7 7 7 9 7 6 6 8 6
## [5473] 7 NA 5 5 6 5 8 10 6 6 6 8 8 7 5 6 7 7 7 8 5 7 7 6
## [5497] 6 8 5 10 8 7 7 8 6 6 9 6 7 6 7 8 10 6 5 7 6 NA 8 10
## [5521] 4 7 8 7 7 8 7 8 4 6 6 7 6 8 7 5 NA 8 7 NA 8 6 9 9
## [5545] 4 7 6 7 6 6 8 5 7 5 9 7 8 7 7 7 9 6 4 6 5 8 7 8
## [5569] 7 NA NA 9 7 9 7 7 6 9 6 7 5 NA 9 8 10 7 9 8 7 8 6 4
## [5593] 6 4 4 8 8 8 8 4 9 8 8 10 8 5 8 5 7 7 5 5 7 9 8 8
## [5617] 5 7 10 7 9 9 8 7 6 7 6 7 5 NA 6 6 6 7 4 6 7 8 NA 6
## [5641] 7 8 9 NA 6 6 9 6 5 7 9 6 6 6 8 7 9 5 6 6 7 8 6 6
## [5665] 8 8 4 7 7 6 6 6 4 6 5 7 5 8 5 9 8 5 7 6 8 10 6 7
## [5689] 9 8 9 8 7 7 5 6 6 6 7 7 NA 8 9 NA NA 8 8 8 9 8 9 7
## [5713] 6 9 10 9 7 9 8 5 7 7 9 7 6 8 4 6 8 7 8 7 7 6 8 5
## [5737] 7 9 6 5 4 NA 8 6 5 7 5 9 4 5 7 8 9 8 9 7 6 9 9 8
## [5761] NA 9 8 7 8 8 8 7 6 9 6 7 NA 9 7 9 10 7 8 8 7 8 8 NA
## [5785] 10 7 9 9 4 9 9 7 8 8 9 6 9 5 4 8 9 7 4 5 8 7 9 7
## [5809] 6 7 9 9 7 7 8 6 8 7 7 7 10 6 6 9 8 5 7 8 6 8 7 6
## [5833] 9 9 7 8 9 6 8 6 5 6 5 8 6 5 8 8 7 6 6 9 6 6 8 8
## [5857] 7 9 6 8 9 6 6 7 7 8 7 7 6 7 9 9 4 6 7 7 7 6 6 6
## [5881] 8 8 6 9 8 6 7 8 5 5 8 6 9 10 8 8 5 5 7 5 7 6 7 7
## [5905] 7 6 5 7 4 9 8 6 8 6 7 6 7 5 7 5 10 NA 7 8 5 6 8 7
## [5929] 6 8 7 8 8 6 7 6 8 8 6 NA 9 7 8 7 7 7 6 7 4 6 8 8
## [5953] NA 8 8 7 6 8 7 6 6 7 9 7 7 8 8 7 NA 6 9 6 9 7 7 8
## [5977] 6 8 7 8 6 6 4 6 6 6 7 8 8 8 NA 7 7 8 8 5 7 4 4 6
## [6001] 7 6 4 8 6 8 6 6 8 6 7 7 8 6 8 5 8 8 7 NA 7 8 6 7
## [6025] 8 8 10 7 NA 6 5 NA 6 7 8 6 6 9czynniki5 <- hotdeck(czynniki4)miss_var_summary(czynniki5)## # A tibble: 40 × 3
## variable n_miss pct_miss
## <chr> <int> <num>
## 1 Hours_Studied 0 0
## 2 Attendance 0 0
## 3 Parental_Involvement 0 0
## 4 Access_to_Resources 0 0
## 5 Extracurricular_Activities 0 0
## 6 Sleep_Hours 0 0
## 7 Previous_Scores 0 0
## 8 Motivation_Level 0 0
## 9 Internet_Access 0 0
## 10 Tutoring_Sessions 0 0
## # ℹ 30 more rowsReguły walidacyjne
rules <- validator(
Hours_Studied >= 0,
Hours_Studied <= 168,
Attendance >= 0,
Attendance <= 100,
Sleep_Hours >= 0,
Sleep_Hours <= 24,
Previous_Scores >= 0,
Previous_Scores <= 100,
Physical_Activity >= 0,
Physical_Activity <= 168,
Exam_Score >= 0,
Exam_Score <= 100,
Sleep_Hours * 7 + Hours_Studied + Physical_Activity >= 0,
Sleep_Hours * 7 + Hours_Studied + Physical_Activity <= 168
)
wyniki <- confront(czynniki5, rules)
summary(wyniki)## name items passes fails nNA error warning
## 1 V01 6038 6038 0 0 FALSE FALSE
## 2 V02 6038 6038 0 0 FALSE FALSE
## 3 V03 6038 6038 0 0 FALSE FALSE
## 4 V04 6038 6038 0 0 FALSE FALSE
## 5 V05 6038 6038 0 0 FALSE FALSE
## 6 V06 6038 6038 0 0 FALSE FALSE
## 7 V07 6038 6038 0 0 FALSE FALSE
## 8 V08 6038 6038 0 0 FALSE FALSE
## 9 V09 6038 6038 0 0 FALSE FALSE
## 10 V10 6038 6038 0 0 FALSE FALSE
## 11 V11 6038 6038 0 0 FALSE FALSE
## 12 V12 6038 6037 1 0 FALSE FALSE
## 13 V13 6038 6038 0 0 FALSE FALSE
## 14 V14 6038 6038 0 0 FALSE FALSE
## expression
## 1 Hours_Studied - 0 >= -1e-08
## 2 Hours_Studied - 168 <= 1e-08
## 3 Attendance - 0 >= -1e-08
## 4 Attendance - 100 <= 1e-08
## 5 Sleep_Hours - 0 >= -1e-08
## 6 Sleep_Hours - 24 <= 1e-08
## 7 Previous_Scores - 0 >= -1e-08
## 8 Previous_Scores - 100 <= 1e-08
## 9 Physical_Activity - 0 >= -1e-08
## 10 Physical_Activity - 168 <= 1e-08
## 11 Exam_Score - 0 >= -1e-08
## 12 Exam_Score - 100 <= 1e-08
## 13 Sleep_Hours * 7 + Hours_Studied + Physical_Activity - 0 >= -1e-08
## 14 Sleep_Hours * 7 + Hours_Studied + Physical_Activity - 168 <= 1e-08plot(wyniki)
dane_zwalidowane <- czynniki5 %>%
replace_errors(rules)
errors_removed(dane_zwalidowane)## call: locate_errors(data, x, ref, ..., cl = cl, Ncpus = Ncpus)
## located 1 error(s).
## located 0 missing value(s).
## Use 'summary', 'values', '$errors' or '$weight', to explore and retrieve the errors.par(mfrow=c(2,3))
boxplot(dane_zwalidowane$Hours_Studied, main="Hours Studied")
boxplot(dane_zwalidowane$Attendance, main="Attendance")
boxplot(dane_zwalidowane$Sleep_Hours, main="Sllep Hours")
boxplot(dane_zwalidowane$Previous_Scores, main="Previos Scores")
boxplot(dane_zwalidowane$Tutoring_Sessions, main="Tutoring Sessions")
boxplot(dane_zwalidowane$Exam_Score, main="Exam Score")
par(mfrow=c(2,3)) #zmienić przy kolejnych wykresach na c(1,1) bo będzie pamiętać i tworzyć wykresy w blokach 6- wykresowych
boxplot(dane_zwalidowane$Hours_Studied, main="Hours Studied")
boxplot(dane_zwalidowane$Attendance, main="Attendance")
boxplot(dane_zwalidowane$Sleep_Hours, main="Sllep Hours")
boxplot(dane_zwalidowane$Previous_Scores, main="Previos Scores")
boxplot(dane_zwalidowane$Tutoring_Sessions, main="Tutoring Sessions")
boxplot(dane_zwalidowane$Exam_Score, main="Exam Score")ggplot(dane_zwalidowane, aes(x=Attendance)) +
geom_boxplot() +
theme_bw() +
coord_flip()
ggplot(dane_zwalidowane, aes(x=Hours_Studied)) +
geom_boxplot() +
theme_bw() +
coord_flip()
ggplot(dane_zwalidowane, aes(x=Sleep_Hours)) +
geom_boxplot() +
theme_bw() +
coord_flip()
ggplot(dane_zwalidowane, aes(x=Previous_Scores)) +
geom_boxplot() +
theme_bw() +
coord_flip()
ggplot(dane_zwalidowane, aes(x=Tutoring_Sessions)) +
geom_boxplot() +
theme_bw() +
coord_flip()
ggplot(dane_zwalidowane, aes(x=Exam_Score)) +
geom_boxplot() +
theme_bw() +
coord_flip()
grubbs.test(dane_zwalidowane$Hours_Studied)##
## Grubbs test for one outlier
##
## data: dane_zwalidowane$Hours_Studied
## G = 4.01539, U = 0.99733, p-value = 0.1773
## alternative hypothesis: highest value 44 is an outliergrubbs.test(dane_zwalidowane$Attendance)##
## Grubbs test for one outlier
##
## data: dane_zwalidowane$Attendance
## G = 1.72722, U = 0.99951, p-value = 1
## alternative hypothesis: lowest value 60 is an outliergrubbs.test(dane_zwalidowane$Sleep_Hours)##
## Grubbs test for one outlier
##
## data: dane_zwalidowane$Sleep_Hours
## G = 2.0552, U = 0.9993, p-value = 1
## alternative hypothesis: lowest value 4 is an outliergrubbs.test(dane_zwalidowane$Previous_Scores)##
## Grubbs test for one outlier
##
## data: dane_zwalidowane$Previous_Scores
## G = 1.7435, U = 0.9995, p-value = 1
## alternative hypothesis: lowest value 50 is an outliergrubbs.test(dane_zwalidowane$Tutoring_Sessions)##
## Grubbs test for one outlier
##
## data: dane_zwalidowane$Tutoring_Sessions
## G = 5.25143, U = 0.99543, p-value = 0.0004415
## alternative hypothesis: highest value 8 is an outliergrubbs.test(dane_zwalidowane$Exam_Score)##
## Grubbs test for one outlier
##
## data: dane_zwalidowane$Exam_Score
## G = 8.40582, U = 0.98829, p-value < 2.2e-16
## alternative hypothesis: highest value 100 is an outlierggplot(dane_zwalidowane, aes(x = Gender, fill = Gender))+
geom_bar()+
scale_fill_manual(values =c("Female"="pink","Male"="lightblue"))+
theme_minimal()+
ggtitle("Podział płci w próbie")+
theme(plot.title = element_text(hjust =0.5))
ggplot(dane_zwalidowane, aes(x = Exam_Score, fill = Exam_Score))+
geom_histogram(binwidth =5,fill="#5C1C81", color ="black")+
theme_minimal()+
ggtitle("Rozkład wyników egzaminów")+
theme(plot.title = element_text(hjust =0.5))## Warning: Removed 1 row containing non-finite outside the scale range
## (`stat_bin()`).
w1 <- ggplot(dane_zwalidowane, aes(x = Exam_Score))+
geom_histogram(binwidth =5, fill ="steelblue", color ="black")+
theme_minimal()+
labs(title ="Rozkład wyników egzaminów", x ="Wynik egzaminu", y ="Liczba uczniów")+
facet_grid(~Gender)
w2 <-ggplot(dane_zwalidowane, aes(x = Hours_Studied))+
geom_histogram(binwidth =5, fill ="darkgreen", color ="black")+
theme_minimal()+
labs(title ="Rozkład godzin nauki", x ="Godziny nauki w tygodniu", y="Liczba uczniów")+
facet_grid(~Gender)
grid.arrange(w1, w2, nrow = 1)## Warning: Removed 1 row containing non-finite outside the scale range
## (`stat_bin()`).
ggplot(dane_zwalidowane, aes(x = Hours_Studied, y = Exam_Score))+
geom_point(color ="blue", alpha =0.6)+
geom_smooth(method ="lm", color ="red", se =FALSE)+
theme_minimal()+
labs(title ="Relacja między godzinami nauki a wynikiem egzaminu",
x ="Godziny nauki w tygodniu",
y ="Wynik egzaminu")## `geom_smooth()` using formula = 'y ~ x'## Warning: Removed 1 row containing non-finite outside the scale range
## (`stat_smooth()`).## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_point()`).
ggplot(dane_zwalidowane, aes(x = Parental_Involvement, y = Exam_Score, fill = Parental_Involvement))+
geom_violin()+
theme_minimal()+
labs(title ="Wyniki egzaminów w zależności od zaangażowania rodziców",
x ="Zaangażowanie rodziców",
y ="Wynik egzaminu")+
scale_fill_brewer(palette ="Set2")## Warning: Removed 1 row containing non-finite outside the scale range
## (`stat_ydensity()`).
# Wykres słupkowy typów szkół
ggplot(dane_zwalidowane, aes(x = School_Type, fill = School_Type))+
geom_bar()+
theme_minimal()+
labs(title ="Rozkład typów szkół",
x ="Typ szkoły",
y ="Liczba uczniów")+
scale_fill_brewer(palette ="Set1")
ggplot(dane_zwalidowane, aes(x = School_Type, y = Exam_Score, fill = School_Type))+
geom_boxplot()+
theme_minimal()+
labs(title ="Wyniki egzaminów w zależności od typów szkół",
x ="Typ Szkoły",
y ="Wynik egzaminu")+
scale_fill_brewer(palette ="Set2")## Warning: Removed 1 row containing non-finite outside the scale range
## (`stat_boxplot()`).
ggplot(dane_zwalidowane, aes(x = Parental_Involvement, y = Exam_Score, fill = Parental_Involvement))+
geom_boxplot()+
facet_wrap(~ Motivation_Level)+
theme_minimal()+
labs(title ="Wyniki egzaminów w zależności od motywacji i zaangażowania rodziców",
x ="Zaangażowanie rodziców",
y ="Wynik egzaminu")+
scale_fill_brewer(palette ="Set3")## Warning: Removed 1 row containing non-finite outside the scale range
## (`stat_boxplot()`).
ggplot(dane_zwalidowane, aes(x = Access_to_Resources, y = Exam_Score, fill = Access_to_Resources))+
geom_boxplot()+
facet_wrap(~ Internet_Access)+
theme_minimal()+
labs(title ="Wyniki egzaminów w zależności od dostępu do źródeł i internetu",
x ="Dostęp do źródeł",
y ="Wynik egzaminu")+
scale_fill_brewer(palette ="Set5")## Warning: Unknown palette: "Set5"## Warning: Removed 1 row containing non-finite outside the scale range
## (`stat_boxplot()`).
ggplot(dane_zwalidowane, aes(x = Exam_Score))+
geom_histogram(binwidth =5, fill ="steelblue", color ="black")+
theme_minimal()+
labs(title ="Rozkład wyników egzaminów", x ="Wynik egzaminu", y ="Liczba uczniów")+
facet_grid(~Learning_Disabilities)## Warning: Removed 1 row containing non-finite outside the scale range
## (`stat_bin()`).
# Wykres heksagonalny
ggplot(dane_zwalidowane, aes(x = Distance_from_Home, y = Exam_Score)) +
geom_hex(bins = 30) + # Liczba przedziałów (możesz dostosować np. 20, 40)
scale_fill_viridis_c() + # Kolorystyka dla lepszej wizualizacji
theme_minimal() +
labs(
title = "Zależność między wynikiem egzaminu a dystansem od domu",
x = "Dystans od domu do szkoły",
y = "Wynik Egzaminu",
fill = "Gęstość"
)## Warning: Removed 1 row containing non-finite outside the scale range
## (`stat_binhex()`).
ld_counts <- dane_zwalidowane %>%
count(Learning_Disabilities)%>%
mutate(Percentage =round(n /sum(n)*100,1))# Zaokrąglamy do 1 miejsca po przecinku# Tworzenie wykresu kołowego
ggplot(ld_counts, aes(x ="", y = n, fill = Learning_Disabilities))+
geom_bar(stat ="identity", width =1)+
coord_polar("y", start =0)+
scale_fill_manual(values =c("Yes"="red","No"="lightblue"))+
theme_void()+
ggtitle("Udział osób z trudnościami w uczeniu się")+
theme(plot.title = element_text(hjust =0.5))+
geom_text(aes(label = paste0(Percentage,"%")),
position = position_stack(vjust =0.5),
color ="black", size =5)
ggplot(dane_zwalidowane, aes(x = Exam_Score))+
geom_histogram(binwidth =5, fill ="darkred", color ="black")+
theme_minimal()+
labs(title ="Rozkład wyników egzaminów", x ="Wynik egzaminu", y ="Poziom wykształcenia rodziców")+
facet_grid(~Parental_Education_Level)## Warning: Removed 1 row containing non-finite outside the scale range
## (`stat_bin()`).
# Upewniamy się, że kategorie są w poprawnej kolejności
dane_zwalidowane$Teacher_Quality <- factor(dane_zwalidowane$Teacher_Quality, levels =c("Low","Medium","High"))# Obliczenie mediany wyników egzaminów dla każdej kategorii jakości nauczycieli
median_scores <- dane_zwalidowane %>%
group_by(Teacher_Quality)%>%
summarise(Median_Exam_Score = median(Exam_Score, na.rm =TRUE))# Wykres liniowy z medianą
ggplot(median_scores, aes(x = Teacher_Quality, y = Median_Exam_Score, group =1))+
geom_line(color ="#ff6347", size =1)+# Linia wykresu
geom_point(color ="darkred", size =3)+# Punkty oznaczające medianę
geom_text(aes(label =round(Median_Exam_Score,1)), vjust =-1)+# Etykiety mediany
ylim(0,100)+# Skala od 0 do 100
theme_minimal()+
ggtitle("Mediana wyniku egzaminu a jakość nauczycieli")+
xlab("Jakość nauczycieli")+
ylab("Mediana wyniku egzaminu")+
theme(plot.title = element_text(hjust =0.5))## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
ggplot(dane_zwalidowane, aes(x = Family_Income, y = Tutoring_Sessions, color = Family_Income)) +
geom_jitter(width = 0.2, alpha = 0.7) + # Dodanie punktów z małym zakłóceniem na osi X (w celu uniknięcia nakładania punktów)
geom_smooth(method = "lm", se = FALSE, color = "black") + # Linia trendu (regresji liniowej)
scale_color_manual(values = c("High" = "lightgreen", "Medium" = "lightblue", "Low" = "lightpink")) +
theme_minimal() +
labs(
title = "Wpływ dochodów rodziny na liczbę korepetycji",
x = "Dochód rodziny",
y = "Liczba korepetycji",
color = "Dochód"
)## `geom_smooth()` using formula = 'y ~ x'
ld_counts <- dane_zwalidowane %>%
count(Family_Income)%>%
mutate(Percentage =round(n /sum(n)*100,1))# Zaokrąglamy do 1 miejsca po przecinku# Tworzenie wykresu kołowego
ggplot(ld_counts, aes(x ="", y = n, fill = Family_Income))+
geom_bar(stat ="identity", width =1)+
coord_polar("y", start =0)+
scale_fill_manual(values =c("Low"="lightpink","Medium"="lightblue","High"="lightgreen"))+
theme_void()+
ggtitle("Poziom dochodów rodziców")+
theme(plot.title = element_text(hjust =0.5))+
geom_text(aes(label = paste0(Percentage,"%")),
position = position_stack(vjust =0.5),
color ="black", size =5)
ggplot(dane_zwalidowane, aes(x = Sleep_Hours, y = Exam_Score)) +
geom_jitter(color = "purple", alpha = 0.5) +
geom_smooth(method = "lm", color = "orange", se = TRUE) +
theme_minimal() +
labs(title = "Relacja między godzinami snu a wynikiem egzaminu",
x = "Godziny snu",
y = "Wynik egzaminu")## `geom_smooth()` using formula = 'y ~ x'
# Używamy Twojego zbioru danych
zmienne_ilosciowe <- dane_zwalidowane %>%
select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores,
Tutoring_Sessions, Physical_Activity, Exam_Score)
data <- zmienne_ilosciowe
# Wyliczenie statystyk opisowych dla zmiennej Hours_Studied
stat_desc <- data %>%
summarise(
średnia = mean(Hours_Studied, na.rm = TRUE),
mediana = median(Hours_Studied, na.rm = TRUE),
odchylenie_standardowe = sd(Hours_Studied, na.rm = TRUE),
minimum = min(Hours_Studied, na.rm = TRUE),
maksimum = max(Hours_Studied, na.rm = TRUE)
) %>%
pivot_longer(
cols = everything(), # Wszystkie kolumny przekształcamy w długą tabelę
names_to = "Statystyka",
values_to = "Wartość"
)
# Tworzenie efektownej tabeli za pomocą gt
stat_desc %>%
gt() %>%
tab_header(
title = "Statystyki Opisowe:",
subtitle = "Hours_Studied"
) %>%
fmt_number(
columns = Wartość,
decimals = 2
) %>%
data_color(
columns = Wartość,
colors = scales::col_numeric(
palette = c("purple", "pink", "lightblue"),
domain = NULL
)
) %>%
cols_label(
Statystyka = "Rodzaj statystyki",
Wartość = "Wartość"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_column_labels()
)## Warning: Since gt v0.9.0, the `colors` argument has been deprecated.
## • Please use the `fn` argument instead.
## This warning is displayed once every 8 hours.| Statystyki Opisowe: | |
| Hours_Studied | |
| Rodzaj statystyki | Wartość |
|---|---|
| średnia | 19.99 |
| mediana | 20.00 |
| odchylenie_standardowe | 5.98 |
| minimum | 1.00 |
| maksimum | 44.00 |
# Używamy Twojego zbioru danych
zmienne_ilosciowe <- dane_zwalidowane %>%
select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores,
Tutoring_Sessions, Physical_Activity, Exam_Score)
data <- zmienne_ilosciowe
# Wyliczenie statystyk opisowych dla zmiennej Attendance
stat_desc <- data %>%
summarise(
średnia = mean(Attendance, na.rm = TRUE),
mediana = median(Attendance, na.rm = TRUE),
odchylenie_standardowe = sd(Attendance, na.rm = TRUE),
minimum = min(Attendance, na.rm = TRUE),
maksimum = max(Attendance, na.rm = TRUE)
) %>%
pivot_longer(
cols = everything(), # Wszystkie kolumny przekształcamy w długą tabelę
names_to = "Statystyka",
values_to = "Wartość"
)
# Tworzenie efektownej tabeli za pomocą gt
stat_desc %>%
gt() %>%
tab_header(
title = "Statystyki Opisowe:",
subtitle = "Attendance"
) %>%
fmt_number(
columns = Wartość,
decimals = 2
) %>%
data_color(
columns = Wartość,
colors = scales::col_numeric(
palette = c("purple", "pink", "lightblue"),
domain = NULL
)
) %>%
cols_label(
Statystyka = "Rodzaj statystyki",
Wartość = "Wartość"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_column_labels()
)| Statystyki Opisowe: | |
| Attendance | |
| Rodzaj statystyki | Wartość |
|---|---|
| średnia | 80.02 |
| mediana | 80.00 |
| odchylenie_standardowe | 11.59 |
| minimum | 60.00 |
| maksimum | 100.00 |
# Używamy Twojego zbioru danych
zmienne_ilosciowe <- dane_zwalidowane %>%
select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores,
Tutoring_Sessions, Physical_Activity, Exam_Score)
data <- zmienne_ilosciowe
# Wyliczenie statystyk opisowych dla zmiennej Sleep_Hours
stat_desc <- data %>%
summarise(
średnia = mean(Sleep_Hours, na.rm = TRUE),
mediana = median(Sleep_Hours, na.rm = TRUE),
odchylenie_standardowe = sd(Sleep_Hours, na.rm = TRUE),
minimum = min(Sleep_Hours, na.rm = TRUE),
maksimum = max(Sleep_Hours, na.rm = TRUE)
) %>%
pivot_longer(
cols = everything(), # Wszystkie kolumny przekształcamy w długą tabelę
names_to = "Statystyka",
values_to = "Wartość"
)
# Tworzenie efektownej tabeli za pomocą gt
stat_desc %>%
gt() %>%
tab_header(
title = "Statystyki Opisowe:",
subtitle = "Sleep_Hours"
) %>%
fmt_number(
columns = Wartość,
decimals = 2
) %>%
data_color(
columns = Wartość,
colors = scales::col_numeric(
palette = c("purple", "pink", "lightblue"),
domain = NULL
)
) %>%
cols_label(
Statystyka = "Rodzaj statystyki",
Wartość = "Wartość"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_column_labels()
)| Statystyki Opisowe: | |
| Sleep_Hours | |
| Rodzaj statystyki | Wartość |
|---|---|
| średnia | 7.03 |
| mediana | 7.00 |
| odchylenie_standardowe | 1.48 |
| minimum | 4.00 |
| maksimum | 10.00 |
# Używamy Twojego zbioru danych
zmienne_ilosciowe <- dane_zwalidowane %>%
select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores,
Tutoring_Sessions, Physical_Activity, Exam_Score)
data <- zmienne_ilosciowe
# Wyliczenie statystyk opisowych dla zmiennej Tutoring_Sessions
stat_desc <- data %>%
summarise(
średnia = mean(Tutoring_Sessions, na.rm = TRUE),
mediana = median(Tutoring_Sessions, na.rm = TRUE),
odchylenie_standardowe = sd(Tutoring_Sessions, na.rm = TRUE),
minimum = min(Tutoring_Sessions, na.rm = TRUE),
maksimum = max(Tutoring_Sessions, na.rm = TRUE)
) %>%
pivot_longer(
cols = everything(), # Wszystkie kolumny przekształcamy w długą tabelę
names_to = "Statystyka",
values_to = "Wartość"
)
# Tworzenie efektownej tabeli za pomocą gt
stat_desc %>%
gt() %>%
tab_header(
title = "Statystyki Opisowe:",
subtitle = "Tutoring_Sessions"
) %>%
fmt_number(
columns = Wartość,
decimals = 2
) %>%
data_color(
columns = Wartość,
colors = scales::col_numeric(
palette = c("purple", "pink", "lightblue"),
domain = NULL
)
) %>%
cols_label(
Statystyka = "Rodzaj statystyki",
Wartość = "Wartość"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_column_labels()
)| Statystyki Opisowe: | |
| Tutoring_Sessions | |
| Rodzaj statystyki | Wartość |
|---|---|
| średnia | 1.50 |
| mediana | 1.00 |
| odchylenie_standardowe | 1.24 |
| minimum | 0.00 |
| maksimum | 8.00 |
# Używamy Twojego zbioru danych
zmienne_ilosciowe <- dane_zwalidowane %>%
select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores,
Tutoring_Sessions, Physical_Activity, Exam_Score)
data <- zmienne_ilosciowe
# Wyliczenie statystyk opisowych dla zmiennej Physical_Activity
stat_desc <- data %>%
summarise(
średnia = mean(Physical_Activity, na.rm = TRUE),
mediana = median(Physical_Activity, na.rm = TRUE),
odchylenie_standardowe = sd(Physical_Activity, na.rm = TRUE),
minimum = min(Physical_Activity, na.rm = TRUE),
maksimum = max(Physical_Activity, na.rm = TRUE)
) %>%
pivot_longer(
cols = everything(), # Wszystkie kolumny przekształcamy w długą tabelę
names_to = "Statystyka",
values_to = "Wartość"
)
# Tworzenie efektownej tabeli za pomocą gt
stat_desc %>%
gt() %>%
tab_header(
title = "Statystyki Opisowe:",
subtitle = "Physical_Activity"
) %>%
fmt_number(
columns = Wartość,
decimals = 2
) %>%
data_color(
columns = Wartość,
colors = scales::col_numeric(
palette = c("purple", "pink", "lightblue"),
domain = NULL
)
) %>%
cols_label(
Statystyka = "Rodzaj statystyki",
Wartość = "Wartość"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_column_labels()
)| Statystyki Opisowe: | |
| Physical_Activity | |
| Rodzaj statystyki | Wartość |
|---|---|
| średnia | 2.97 |
| mediana | 3.00 |
| odchylenie_standardowe | 1.03 |
| minimum | 0.00 |
| maksimum | 6.00 |
# Używamy Twojego zbioru danych
zmienne_ilosciowe <- dane_zwalidowane %>%
select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores,
Tutoring_Sessions, Physical_Activity, Exam_Score)
data <- zmienne_ilosciowe
# Wyliczenie statystyk opisowych dla zmiennej PExam_Score
stat_desc <- data %>%
summarise(
średnia = mean(Exam_Score, na.rm = TRUE),
mediana = median(Exam_Score, na.rm = TRUE),
odchylenie_standardowe = sd(Exam_Score, na.rm = TRUE),
minimum = min(Exam_Score, na.rm = TRUE),
maksimum = max(Exam_Score, na.rm = TRUE)
) %>%
pivot_longer(
cols = everything(), # Wszystkie kolumny przekształcamy w długą tabelę
names_to = "Statystyka",
values_to = "Wartość"
)
# Tworzenie efektownej tabeli za pomocą gt
stat_desc %>%
gt() %>%
tab_header(
title = "Statystyki Opisowe:",
subtitle = "Exam_Score"
) %>%
fmt_number(
columns = Wartość,
decimals = 2
) %>%
data_color(
columns = Wartość,
colors = scales::col_numeric(
palette = c("purple", "pink", "lightblue"),
domain = NULL
)
) %>%
cols_label(
Statystyka = "Rodzaj statystyki",
Wartość = "Wartość"
) %>%
tab_style(
style = cell_text(weight = "bold"),
locations = cells_column_labels()
)| Statystyki Opisowe: | |
| Exam_Score | |
| Rodzaj statystyki | Wartość |
|---|---|
| średnia | 67.25 |
| mediana | 67.00 |
| odchylenie_standardowe | 3.90 |
| minimum | 56.00 |
| maksimum | 100.00 |
# Statystyki opisowe dla zmiennych ilościowych
zmienne_ilosciowe <- dane_zwalidowane %>%
select(Hours_Studied, Attendance, Sleep_Hours, Previous_Scores,
Tutoring_Sessions, Physical_Activity, Exam_Score)
#. Macierz korelacji dla zmiennych ilościowych
macierz_korelacji <- cor(zmienne_ilosciowe, use = "complete.obs")
print(macierz_korelacji)## Hours_Studied Attendance Sleep_Hours Previous_Scores
## Hours_Studied 1.000000000 -0.001527627 0.014801867 0.017698977
## Attendance -0.001527627 1.000000000 -0.021754266 -0.016306714
## Sleep_Hours 0.014801867 -0.021754266 1.000000000 -0.019589068
## Previous_Scores 0.017698977 -0.016306714 -0.019589068 1.000000000
## Tutoring_Sessions -0.013941975 0.014743286 -0.007150278 -0.020365357
## Physical_Activity 0.005044221 -0.018809595 -0.005467017 -0.005460835
## Exam_Score 0.418862859 0.553354853 -0.016444605 0.164453099
## Tutoring_Sessions Physical_Activity Exam_Score
## Hours_Studied -0.013941975 0.005044221 0.41886286
## Attendance 0.014743286 -0.018809595 0.55335485
## Sleep_Hours -0.007150278 -0.005467017 -0.01644460
## Previous_Scores -0.020365357 -0.005460835 0.16445310
## Tutoring_Sessions 1.000000000 0.015166600 0.13953924
## Physical_Activity 0.015166600 1.000000000 0.03247969
## Exam_Score 0.139539241 0.032479693 1.00000000# Wizualizacja macierzy korelacji
corrplot(macierz_korelacji, method = "circle", type = "upper",
tl.col = "black", tl.srt = 45, col = colorRampPalette(c("blue", "white", "red"))(200))